on the joint distribution of the maximum and its position of the airy2 process minus a parabola the maximal point of the airy2 process minus a parabola is believed to describe the scaling limit of the end point of the directed polymer in a random medium this was proved to be true for a few specific cases recently two different formulas for the joint distribution of the location and the height of this maximal point were obtained one by moreno flores quastel and remenik and the other by schehr the first formula is given in terms of the airy function and an associated operator and the second formula is expressed in terms of the lax pair equations of the painleve ii equation we give a direct proof that these two formulas are the same

markov processes of infinitely many nonintersecting random walks consider an n dimensional markov chain obtained from n one dimensional random walks by doob h transform with the q vandermonde determinant we prove that as n becomes large these markov chains converge to an infinite dimensional feller markov process the dynamical correlation functions of the limit process are determinantal with an explicit correlation kernel the key idea is to identify random point processes on z with q gibbs measures on gelfand tsetlin schemes and construct markov processes on the latter space independently we analyze the large time behavior of pushasep with finitely many particles and particle dependent jump rates it arises as a marginal of our dynamics on gelfand tsetlin schemes the asymptotics is given by a product of a marginal of the gue minor process and geometric distributions

a pde for the multi time joint probability of the airy process abstract this paper gives a pde for multi time joint probability of the airy process which generalizes adler and van moerbeke s result on the 2 time case as an intermediate step the pde for the multi time joint probability of the dyson brownian motion is also given

non linear pdes for gap probabilities in random matrices and kp theory abstract airy and pearcey like kernels and generalizations arising in random matrix theory are expressed as double integrals of ratios of exponentials possibly multiplied with a rational function in this work it is shown that such kernels are intimately related to wave functions for polynomial gelfand dickey reductions or rational reductions of the kp hierarchy their fredholm determinant also satisfies linear pdes virasoro constraints yielding in a systematic way non linear pdes for the fredholm determinant of such kernels examples include fredholm determinants giving the gap probability of some infinite dimensional diffusions like the airy process with or without outliers and the pearcey process with or without inliers

dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition the one dimensional totally asymmetric simple exclusion process tasep is considered we study the time evolution property of a tagged particle in the tasep with the step initial condition calculated is the multi time joint distribution function of its position using the relation of the dynamics of the tasep to the schur process we show that the function is represented as the fredholm determinant we also study the scaling limit the universality of the largest eigenvalue in the random matrix theory is realized in the limit when the hopping rates of all particles are the same it is found that the joint distribution function converges to that of the airy process after the time at which the particle begins to move on the other hand when there are several particles with small hopping rate in front of a tagged particle the limiting process changes at a certain time from the airy process to the process of the largest eigenvalue in the hermitian multi matrix model with external sources

limiting distribution of maximal crossing and nesting of poissonized random matchings the notion of r crossing and r nesting of a complete matching was introduced and a symmetry property was proved by chen et al trans amer math soc 359 2007 1555 1575 we consider random matchings of large size and study their maximal crossing and their maximal nesting it is known that the marginal distribution of each of them converges to the goe tracy widom distribution we show that the maximal crossing and the maximal nesting becomes independent asymptotically and we evaluate the joint distribution for the poissonized random matchings explicitly to the first correction term this leads to an evaluation of the asymptotic of the covariance furthermore we compute the explicit second correction term in the distribution function of two objects a the length of the longest increasing subsequence of poissonized random permutation and b the maximal crossing and hence also the maximal nesting of poissonized random matching

step fluctuations for a faceted crystal a statistical mechanics model for a faceted crystal is the 3d ising model at zero temperature it is assumed that in one octant all sites are occupied by atoms the remaining ones being empty allowed atom configurations are such that they can be obtained from the filled octant through successive removals of atoms with breaking of precisely three bonds if v denotes the number of atoms removed then the grand canonical boltzmann weight is q v 0 q 1 as shown by cerf and kenyon in the limit q 1 a deterministic shape is attained which has the three facets 100 010 001 and a rounded piece interpolating between them we analyse the step statistics as q 1 in the rounded piece it is given by a determinantal process based on the discrete sine kernel exactly at the facet edge the steps have more space to meander their statistics is again determinantal but this time based on the airy kernel in particular the border step is well approximated by the airy process which has been obtained previously in the context of growth models our results are based on the asymptotic analysis for space time inhomogeneous transfer matrices

gibbs ensembles of nonintersecting paths we consider a family of determinantal random point processes on the two dimensional lattice and prove that members of our family can be interpreted as a kind of gibbs ensembles of nonintersecting paths examples include probability measures on lozenge and domino tilings of the plane some of which are non translation invariant the correlation kernels of our processes can be viewed as extensions of the discrete sine kernel and we show that the gibbs property is a consequence of simple linear relations satisfied by these kernels the processes depend on infinitely many parameters which are closely related to parametrization of totally positive toeplitz matrices

on the computational efficiency of multiple objective metaheuristics the knapsack problem case study abstract the paper describes a computational experiment which goal is to evaluate computational efficiency of three multiple objective evolutionary metaheuristics on the multiple objective multiple constraints knapsack problem the relative efficiency of the multiple objective algorithms is evaluated with respect to a single objective evolutionary algorithm ea we use a methodology that allows consistent evaluation of the quality of approximately pareto optimal solutions generated by both multiple and single objective metaheuristics then we compare computational efforts needed to generate solutions of approximately the same quality by the two kinds of methods the results indicate that computational efficiency of multiple objective eas deteriorates with the growth of the number of objectives furthermore significant differences in the performance of the three algorithms are observed

the arctic circle boundary and the airy process we prove that the appropriately rescaled boundary of the north polar region in the aztec diamond converges to the airy process the proof uses certain determinantal point processes given by the extended krawtchouk kernel we also prove a version of propp s conjecture concerning the structure of the tiling at the center of the aztec diamond 1 introduction and results domino tilings of the aztec diamond were introduced in 8 9 asymptotic properties of random domino tilings of the aztec diamond have been studied in 5 12 15 in particular in 12 the existence of the so called arctic circle was proved the arctic circle is the asymptotic boundary of the disordered so called temperate region of the tiling outside this boundary the tiling forms a completely regular brick wall pattern the methods in 12 combined with the results in 13 show that the fluctuations of the point of intersection of the boundary of the temperate region with a line converge to the tracy widom distribution of random matrix theory in this paper we extend this result to show that the fluctuations of the boundary around the arctic circle converges to the airy process introduced in 23 the paper is a continuation of the approach used in 14 and 15 where certain point processes with determinantal correlation functions 24 and the krawtchouk ensemble were used we will use the general techniques developed in 16 and investigate an extended point process which also has determinantal correlation functions given by a kernel which we call the extended krawtchouk kernel the aztec diamond an of order n is the union of all lattice squares m m 1 l l 1 m l 2 z that lie inside the region x1 y1 x1 y1

non intersecting paths random tilings and random matrices we investigate certain measures induced by families of non intersecting paths in domino tilings of the aztec diamond rhombus tilings of an abc hexagon a dimer model on a cylindrical brick lattice and a growth model the measures obtained e g the krawtchouk and hahn ensembles have the same structure as the eigenvalue measures in random matrix theory like gue which can in fact can be obtained from non intersecting brownian motions the derivations of the measures are based on the karlin mcgregor or lindstrom gessel viennot method we use the measures to show some asymptotic results for the models

airy processes with wanderers and new universality classes consider n m nonintersecting brownian bridges with n of them leaving from 0 at time t 1 and returning to 0 at time t 1 while the m remaining ones wanderers go from m points a i to m points b i first we keep m fixed and we scale a i b i appropriately with n in the large n limit we obtain a new airy process with wanderers in the neighborhood of root 2n the approximate location of the rightmost particle in the absence of wanderers this new process is governed by an airy type kernel with a rational perturbation letting the number m of wanderers tend to infinity as well leads to two pearcey processes about two cusps a closing and an opening cusp the location of the tips being related by an elliptic curve upon tuning the starting and target points one can let the two tips of the cusps grow very close this leads to a new process which might be governed by a kernel represented as a double integral involving the exponential of a quintic polynomial in the integration variables

dyson s nonintersecting brownian motions with a few outliers consider n nonintersecting brownian particles on r dyson brownian motions all starting from the origin at time t 0 and forced to return to x 0 at time t 1 for large n the average mean density of particles has its support for each 0 0 does it affect the brownian fluctuations along the curve c for large n in this paper we show that no new process appears as long as one considers points y t is an element of c such that 0 infinity this kernel is closely related to one found by baik ben arous and peche in the context of multivariate statistics c 2008 wiley periodicals inc

schur dynamics of the schur processes abstract we construct discrete time markov chains that preserve the class of schur processes on partitions and signatures one application is a simple exact sampling algorithm for q volume distributed skew plane partitions with an arbitrary back wall another application is a construction of markov chains on infinite gelfand tsetlin schemes that represent deterministic flows on the space of extreme characters of the infinite dimensional unitary group

the generalized logit linear item response model for binary designed items this paper introduces the generalized logit linear item response model gllirm which represents the item solving process as a series of dichotomous operations or steps the gllirm assumes that the probability function of the item response is a logistic function of a linear composite of basic parameters which describe the operations and the coefficients depend on three design matrices x y and z the gllirm provides a tool for testing hypotheses on the item solving process and generalizes existing models an empirical application is included in which the model is applied to evaluate sources of difficulty and pairwise item interactions in a logical analysis test

the arctic curve of the domain wall six vertex model the problem of the form of the arctic curve of the six vertex model with domain wall boundary conditions in its disordered regime is addressed it is well known that in the scaling limit the model exhibits phase separation with regions of order and disorder sharply separated by a smooth curve called the arctic curve to find this curve we study a multiple integral representation for the emptiness formation probability a correlation function devised to detect spatial transition from order to disorder we conjecture that the arctic curve for arbitrary choice of the vertex weights can be characterized by the condition of condensation of almost all roots of the corresponding saddle point equations at the same known value in explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle point equations the arctic curve is obtained in parametric form and appears to be a non algebraic curve in general it turns into an algebraic one in the so called root of unity cases the arctic curve is also discussed in application to the limit shape of q enumerated with 0 q 4 large alternating sign matrices in particular as q 0 the limit shape tends to a nontrivial limiting curve given by a relatively simple equation

non colliding paths in the honeycomb dimer model and the dyson process in this paper we describe a natural family of random non intersecting discrete paths in the dimer model on the honeycomb lattice we show that when the dimer model is going to freeze this family of paths after a proper rescaling converges to the extended sine process obtained traditionally as the limit of the dyson model when the number of particles goes to infinity

polynuclear growth on a flat substrate and edge scaling of goe eigenvalues we consider the polynuclear growth png model in 1 1 dimension with flat initial condition and no extra constraints through the robinson schensted knuth rsk construction one obtains the multilayer png model which consists of a stack of non intersecting lines the top one being the png height the statistics of the lines is translation invariant and at a fixed position the lines define a point process we prove that for large times the edge of this point process suitably scaled has a limit this limit is a pfaffian point process and identical to the one obtained from the edge scaling of the gaussian orthogonal ensemble goe of random matrices our results give further insight to the universality structure within the kpz class of 1 1 dimensional growth models

arctic circles domino tilings and square young tableaux the arctic circle theorem of jockusch propp and shor asserts that uniformly random domino tilings of an aztec diamond of high order are frozen with asymptotically high probability outside the arctic circle inscribed within the diamond a similar arctic circle phenomenon has been observed in the limiting behavior of random square young tableaux in this paper we show that random domino tilings of the aztec diamond are asymptotically related to random square young tableaux in a more refined sense that looks also at the behavior inside the arctic circle this is done by giving a new derivation of the limiting shape of the height function of a random domino tiling of the aztec diamond that uses the large deviation techniques developed for the square young tableaux problem in a previous paper by pittel and the author the solution of the variational problem that arises for domino tilings is almost identical to the solution for the case of square young tableaux by pittel and the author the analytic techniques used to solve the variational problem provide a systematic guess free approach for solving problems of this type which have appeared in a number of related combinatorial probability models

scale invariance of the png droplet and the airy process we establish that the static height fluctuations of a particular growth model the png droplet converges upon proper rescaling to a limit process which we call the airy process a y the airy process is stationary it has continuous sample paths its single time fixed y distribution is the tracy widom distribution of the largest eigenvalue of a gue random matrix and the airy process has a slow decay of correlations as y 2 roughly the airy process describes the last line of dyson s brownian motion model for random matrices our construction uses a multi layer version of the png model which can be analyzed through fermionic techniques specializing our result to a fixed value of y one reobtains the celebrated result of baik deift and johansson on the length of the longest increasing subsequence of a random permutation

marginal maximum likelihood estimation for the one parameter logistic model two algorithms are described for marginal maximum likelihood estimation for the one parameter logistic model the more efficient of the two algorithms is extended to estimation for the linear logistic model numerical examples of both procedures are presented

interquad an interactive quad tree based procedure for solving the discrete alternative multiple criteria problem abstract in this paper an interactive procedure based upon a data structure called a quad tree is developed for solving the discrete alternative multiple criteria problem called interquad the procedure has been designed with large discrete alternative problems in mind interquad takes advantage of the ability of a quad tree to identify store and retrieve nondominated criterion vectors then the user interacts with the nondominated criterion vectors stored in the quad tree in a fashion similar to that of the combined tchebycheff aspiration criterion vector procedure of steuer silverman and whisman

a periodic hexagon tiling model and non hermitian orthogonal polynomials we study a one parameter family of probability measures on lozenge tilings of large regular hexagons that interpolates between the uniform measure on all possible tilings and a particular fully frozen tiling the description of the asymptotic behavior can be separated into two regimes the low and the high temperature regime our main results are the computations of the disordered regions in both regimes and the limiting densities of the different lozenges there for low temperatures the disordered region consists of two disjoint ellipses in the high temperature regime the two ellipses merge into a single simply connected region at the transition from the low to the high temperature a tacnode appears the key to our asymptotic study is a recent approach introduced by duits and kuijlaars providing a double integral representation for the correlation kernel one of the factors in the integrand is the christoffel darboux kernel associated to polynomials that satisfy non hermitian orthogonality relations with respect to a complex valued weight on a contour in the complex plane we compute the asymptotic behavior of these orthogonal polynomials and the christoffel darboux kernel by means of a riemann hilbert analysis after substituting the resulting asymptotic formulas into the double integral we prove our main results by classical steepest descent arguments

a multiple criteria method for choosing among discrete alternatives abstract an interactive method is presented for solving a discrete alternative multiple criteria problem under certainty the method is based on the approach of zionts and wallenius a computer program embodying the method has been written and the results to date have been favorable extensions to the case in which some of the criteria are not readily quantifiable are also considered

an item response model for nominal data based on the rising selection ratios criterion complete response vectors of all answer options in multiple choice items can be used to estimate ability the rising selection ratios criterion is necessary for scoring individuals because it implies that estimated ability always increases when the correct alternative is selected this paper introduces the generalized dlt model which assumes rising selection ratios and uses three parameters to describe each incorrect alternative it is shown that the nominal categories and the thissen and steinberg model do not meet the criterion a simulation study on goodness of recovery and an example with real data are also included

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

a response model for multiple choice items in the mid 1960s samejima initiated the development of item response models that involve separate response functions for all of the alternatives in the multiple choice and likert type formats her work in this area began at the educational testing service and continued during a visit to the l l thurstone psychometric laboratory at the university of north carolina both samejima s 1969 this volume original model for graded item responses and bock s 1972 this volume model for nominal responses were originally intended to produce response functions for all of the alternatives of multiple choice items for various reasons neither model has proved entirely satisfactory for that purpose although both have been applied in other contexts using a combination of ideas suggested by bock 1972 and samejima 1968 1979 a multiple choice model was developed that produces response functions that fit unidimensional multiple choice tests better thissen and steinberg 1984 that model is the subject of this chapter

tacnode gue minor processes and double aztec diamonds we study determinantal point processes arising in random domino tilings of a double aztec diamond a region consisting of two overlapping aztec diamonds at a turning point in a single aztec diamond where the disordered region touches the boundary the natural limiting process is the gue minor process increasing the size of a double aztec diamond while keeping the overlap between the two aztec diamonds finite we obtain a new determinantal point process which we call the tacnode gue minor process this process can be thought of as two colliding gue minor processes as part of the derivation of the particle kernel whose scaling limit naturally gives the tacnode gue minor process we find the inverse kasteleyn matrix for the dimer model version of the double aztec diamond

spatial correlations of the 1d kpz surface on a flat substrate we study the spatial correlations of the one dimensional kpz surface for the flat initial condition it is shown that the multi point joint distribution for the height is given by a fredholm determinant with its kernel in the scaling limit explicitly obtained this may also describe the dynamics of the largest eigenvalue in the goe dyson s brownian motion model our analysis is based on a reformulation of the determinantal green s function for the totally asep in terms of a vicious walk problem

markov processes on partitions we introduce and study a family of markov processes on partitions the processes preserve the so called z measures on partitions previously studied in connection with harmonic analysis on the infinite symmetric group we show that the dynamical correlation functions of these processes have determinantal structure and we explicitly compute their correlation kernels we also compute the scaling limits of the kernels in two different regimes the limit kernels describe the asymptotic behavior of large rows and columns of the corresponding random young diagrams and the behavior of the young diagrams near the diagonal

a combined tchebycheff aspiration criterion vector interactive multiobjective programming procedure in this paper we combine the tchebycheff method of steuer and choo with wierzbicki s aspiration criterion vector method in order to form an improved procedure for interactive multiple objective programming the combined procedure is sensible because the tchebycheff and aspiration criterion vector methods possess complementary distinguishing characteristics solve similar optimization problems to probe the nondominated set and share a similar computer user interface in the early iterations tchebycheff probes of the nondominated set might be conducted to locate promising neighborhoods of search in later iterations aspiration criterion vector probes might be used to pinpoint a final solution computational experience is reported showing the improved effectiveness of the combined procedure when employed in this fashion when compared against the tchebycheff and aspiration criterion vector methods run separately

gues and queues consider the process d k k 1 2 given by b i being independent standard brownian motions this process describes the limiting behavior near the edge in queues in series totally asymmetric exclusion processes or oriented percolation the problem of finding the distribution of d was posed in gw the main result of this paper is that the process d has the law of the process of the largest eigenvalues of the main minors of an infinite random matrix drawn from gaussian unitary ensemble

double aztec diamonds and the tacnode process discrete and continuous non intersecting random processes have given rise to critical infinite dimensional diffusions like the airy process the pearcey process and variations thereof it has be

random skew plane partitions and the pearcey process we study random skew 3d partitions weighted by qvol and specifically the q 1 asymptotics of local correlations near various points of the limit shape we obtain sine kernel asymptotics for correlations in the bulk of the disordered region airy kernel asymptotics near a general point of the frozen boundary and a pearcey kernel asymptotics near a cusp of the frozen boundary

insdecm an interactive procedure for stochastic multicriteria decision problems abstract a new interactive technique for a discrete stochastic multiattribute decision making problem is proposed in this paper it is assumed that performance probability distribution for each action on each attribute is known two concepts are combined in the procedure stochastic dominance and interactive approach the first one is employed for generating efficient actions and constructing rankings of actions with respect to attributes the second concept is used when the communication between the dm and the model is conducted it is assumed that decision maker s restrictions are defined by specifying minimal or maximal values of scalar criteria measuring either expected outcome or variability of outcomes as such restrictions are in general not consistent with stochastic dominance rules we suggest verifying this consistency and asking the decision maker to redefine inconsistent restrictions

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

solving the discrete multiple criteria problem using convex cones an interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi concave increasing utility or value function the method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions the maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker responses are used to eliminate alternatives using convex cones based on expressed preferences and then a new set of weights is found that satisfies the indicated preferences the requisite theory and proofs as well as a detailed numerical example are included in addition the results of some computational experiments to test the effectiveness of the method are described

large gap asymptotics for airy kernel determinants with discontinuities we obtain large gap asymptotics for airy kernel fredholm determinants with any number m of discontinuities these m point determinants are generating functions for the airy point process and encode probabilistic information about eigenvalues near soft edges in random matrix ensembles our main result is that the m point determinants can be expressed asymptotically as the product of m 1 point determinants multiplied by an explicit constant pre factor which can be interpreted in terms of the covariance of the counting function of the process

probability distributions related to tilings of non convex polygons in this paper we study random lozenge tilings of non convex polygonal regions the interaction of the non convexities cuts leads to new kernels and thus new statistics for the tiling fluctuations near these regions this paper gives new probability distributions and joint probability distributions for the fluctuation of tiles along lines in between the cuts

transition between airy1 and airy2 processes and tasep fluctuations we consider the totally asymmetric simple exclusion process a model in the kpz universality class we focus on the fluctuations of particle positions starting with certain deterministic initial conditions for large time t one has regions with constant and linearly decreasing density the fluctuations on these two regions are given by the airy1 and airy2 processes whose one point distributions are the goe and gue tracy widom distributions of random matrix theory in this paper we analyze the transition region between these two regimes and obtain the transition process its one point distribution is a new interpolation between goe and gue edge distributions 2007 wiley periodicals inc

estimating latent distributions consider vectors of item responses obtained from a sample of subjects from a population in which ability is distributed with densityg where the are unknown parameters assuming the responses depend on through a fully specified item response model this paper presents maximum likelihood equations for the estimation of the population parameters directly from the observed responses i e without estimating an ability parameter for each subject also provided are asymptotic standard errors and tests of fit computing approximations and details of four special cases a non parametric approximation a normal solution a resolution of normal components and a beta binomial solution

tilings of non convex polygons skew young tableaux and determinantal processes this paper studies random lozenge tilings of general non convex polygonal regions we show that the pairwise interaction of the non convexities leads asymptotically to new kernels and thus to new statistics for the tiling fluctuations the precise geometrical figure here consists of a hexagon with cuts along opposite edges for this model we take limits when the size of the hexagon and the cuts tend to infinity while keeping certain geometric data fixed in order to guarantee sufficient interaction between the cuts in the limit we show in this paper that the kernel for the finite tiling model can be expressed as a multiple integral where the number of integrations is related to the fixed geometric data above the limiting kernel is believed to be a universal master kernel

directed last passage percolation and random matrices this paper is a survey of various techniques recent results and applications of directed last passage percolation model and its relation to random matrices the connection can be explained mainly via the universality of famous tracy widom distribution and airy process some unsolved problems are also surveyed

local characteristics entropy and limit theorems for spanning trees and domino tilings via transfer impedances let g be a finite graph or an infinite graph on which mathbb z d acts with finite fundamental domain if g is finite let mathbf t be a random spanning tree chosen uniformly from all spanning trees of g if g is infinite methods from pemantle show that this still makes sense producing a random essential spanning forest of g a method for calculating local characteristics i e finite dimensional marginals of mathbf t from the transfer impedance matrix is presented this differs from the classical matrix tree theorem in that only small pieces of the matrix n dimensional minors are needed to compute small n dimensional marginals calculation of the matrix entries relies on the calculation of the green s function for g which is not a local calculation however it is shown how the calculation of the green s function may be reduced to a finite computation in the case when g is an infinite graph admitting a z d action with finite quotient the same computation also gives the entropy of the law of mathbf t these results are applied to the problem of tiling certain lattices by dominos the so called dimer problem another application of these results is to prove modified versions of conjectures of aldous on the limiting distribution of degrees of a vertex and on the local structure near a vertex of a uniform random spanning tree in a lattice whose dimension is going to infinity included is a generalization of moments to tree valued random variables and criteria for these generalized moments to determine a distribution

aspiration level approach in stochastic mcdm problems the paper considers a discrete stochastic multiple criteria decision making problem this problem is defined by a finite set of actions a a set of attributes x and a set of evaluations of actions with respect to attributes e in stochastic case the evaluation of each action with respect to each attribute takes form of a probability distribution thus the comparison of two actions leads to the comparison of two vectors of probability distributions in the paper a new procedure for solving this problem is proposed it is based on three concepts stochastic dominance interactive approach and preference threshold the idea of the procedure comes from the interactive multiple objective goal programming approach the set of actions is progressively reduced as the decision maker specifies additional requirements at the beginning the decision maker is asked to define preference threshold for each attribute next at each iteration the decision maker is confronted with the set of considered actions if the decision maker is able to make a final choice then the procedure ends otherwise he she is asked to specify aspiration level a didactical example is presented to illustrate the proposed technique

discrete polynuclear growth and determinantal processes we consider a discrete polynuclear growth png process and prove a functional limit theorem for its convergence to the airy process this generalizes previous results by prahofer and spohn the result enables us to express the f1 goe tracy widom distribution in terms of the airy process we also show some results and give a conjecture about the transversal fluctuations in a point to line last passage percolation problem furthermore we discuss a rather general class of measures given by products of determinants and show that these measures have determinantal correlation functions

correlation functions for determinantal processes defined by infinite block toeplitz minors abstract we study the correlation functions for determinantal point processes defined by products of infinite minors of block toeplitz matrices the motivation for studying such processes comes from doubly periodically weighted tilings of planar domains such as the two periodic aztec diamond our main results are double integral formulas for the correlation kernels in general the integrand is a matrix valued function built out of a factorization of the matrix valued weight in concrete examples the factorization can be worked out in detail and we obtain explicit integrands in particular we find an alternative proof for a formula for the two periodic aztec diamond recently derived in 20 we strongly believe that also in other concrete cases the double integral formulas are good starting points for asymptotic studies

exact solutions for kpz type growth processes random matrices and equilibrium shapes of crystals abstract three models from statistical physics can be analyzed by employing space time determinantal processes 1 crystal facets in particular the statistical properties of the facet edge and equivalently tilings of the plane 2 one dimensional growth processes in the kardar parisi zhang universality class and directed last passage percolation 3 random matrices multi matrix models and dyson s brownian motion we explain the method and survey results of physical interest

limit shapes and local statistics for the stochastic six vertex model in this paper we consider the stochastic six vertex model on a cylinder with arbitrary initial data first we show that it exhibits a limit shape in the thermodynamic limit whose density profile is given by the entropy solution to an explicit non linear conservation law that was predicted by gwa spohn phys rev lett 68 725 728 1992 and by reshetikhin sridhar commun math phys 363 741 765 2018 then we show that the local statistics of this model around any continuity point of its limit shape are given by an infinite volume translation invariant gibbs measure of the appropriate slope

a variational principle for domino tilings 1 1 description of results a domino is a 1 x 2 or 2 x 1 rectangle and a tiling of a region by dominos is a way of covering that region with dominos so that there are no gaps or overlaps in 1961 kasteleyn kal found a formula for the number of domino tilings of an m x n rectangle with mn even as shown in figure 1 for rm n 68 temperley and fisher tf used a differenit method and arrived at the same result at almost exactly the same time both lines of calculation showed that the logarithm of number of tilings divided by the number of dominos in a tiling that is mn 2 converges to 2g 7r 0 58 here g is catalan s constant on the other hand in 1992 elkies et al eklp studied domino tilings of regions they called aztec diamonds figure 2 shows an aztec diamond of order 48 and showed that the logarithm of the number of tilings divided by the number of dominos converges to the smaller number log 2 2 0 35 thus even though the region in figure 1 has slightly smaller area than the region in figure 2 the former has far more domino tilings for regions with other shapes neither of these asymptotic formulas may apply in the present paper we consider simply connected regions of arbitrary shape we give an exact formula for the limiting value of the logarithm of the number of tilings per unit area as a function of the shape of the boundary of the region as the size of the region goes to infinity in particular we show that computation of this limit is intimately linked with an understanding of long range variations in the local statistics of random domino tilings such variations can be seen by comparing figures 1 and 2 each of the two tilings is random in the sense that the algorithm pwi that was used to create it generates each of the possible tilings of the region being tiled with the same probability hence one can expect each tiling to be qualitatively typical of the overwhelming majority of tilings of the region in

on the unidentifiability of the fixed effects 3pl model the paper offers a general review of the basic concepts of both statistical model and parameter identification and revisits the conceptual relationships between parameter identification and both parameter interpretability and properties of parameter estimates all these issues are then exemplified for the 1pl 2pl and 1pl g fixed effects models for the 3pl model however we provide a theorem proving that the item parameters are not identified do not have an empirical interpretation and that it is not possible to obtain consistent and unbiased estimates of them

riemann hilbert approach to multi time processes the airy and the pearcey cases we prove that matrix fredholm determinants related to multi time processes can be expressed in terms of determinants of integrable kernels a la its izergin korepin slavnov iiks and hence related to suitable riemann hilbert problems thus extending the known results for the single time case we focus on the airy and pearcey processes as an example of applications we re deduce a third order pde found by adler and van moerbeke for the two time airy process

nonintersecting paths pfaffians and plane partitions gessel and viennot have developed a powerful technique for enumerating various classes of plane partitions the purpose of this article is to show by similar means that one may use pfaffiants to enumerate configurations of nonintersecting paths in which the initial and or terminal vertices of the paths are allowed to vary over specified regions of the digraph this leads to the possibility of enumerating classes of plane partitions in which the shape is allowed to vary whereas the previous applications of gessel and viennot were largely confined to plane partitions of a given shape

asymptotics for the covariance of the airy2 process in this paper we compute some of the higher order terms in the asymptotic be havior of the two point function p a2 0 s1 a2 t s2 extending the previous work of adler and van moerbeke arxiv math pr 0302329 ann probab 33 1326 1361 2005 a nd widom j stat phys 115 1129 1134 2004 we prove that it is possible to represent any order asymptotic approximation as a polynomial and integrals of the painleve ii function q and its derivative q further for up to tenth order we give this asymptotic approximation as a linear combination of the tracy widom gue density function f2 and its derivatives as a corollary to this the asymptotic covariance is expressed up to tenth order in terms of the moments of the tracy widom gue distribution

arctic curves of the twenty vertex model with domain wall boundaries we use the tangent method to compute the arctic curve of the twenty vertex 20v model with particular domain wall boundary conditions for a wide set of integrable weights to this end we extend to the finite geometry of domain wall boundary conditions the standard connection between the bulk 20v and 6v models via the kagome lattice ice model this allows to express refined partition functions of the 20v model in terms of their 6v counterparts leading to explicit parametric expressions for the various portions of its arctic curve the latter displays a large variety of shapes depending on the weights and separates a central liquid phase from up to six different frozen phases a number of numerical simulations are also presented which highlight the arctic curve phenomenon and corroborate perfectly the analytic predictions of the tangent method we finally compute the arctic curve of the quarter turn symmetric holey aztec domino tiling qthadt model a problem closely related to the 20v model and whose asymptotics may be analyzed via a similar tangent method approach again results for the qthadt model are found to be in perfect agreement with our numerical simulations

estimating difficulty from polytomous categorical data a comprehensive analysis of difficulty for multiple choice items requires information at different levels the test the items and the alternatives this paper introduces a new parameterization of the nominal categories model ncm for analyzing difficulty at these three levels the new parameterization is referred to as the ne ncm and is statistically equivalent to the ncm the ne ncm is applied to a sample of responses from a logical analysis test the results suggest that the individuals execute a self terminated response process that is mostly determined by working memory load

coupling functions for domino tilings of aztec diamonds the inverse kasteleyn matrix of a bipartite graph holds much information about the perfect matchings of the system such as local statistics which can be used to compute local and global asymptotics in this paper we consider three different weightings of domino tilings of the aztec diamond and show using recurrence relations that we can compute the inverse kasteleyn matrix these weights are the one periodic weighting where the horizontal edges have one weight and the vertical edges have another weight the qvol weighting which corresponds to multiplying the product of tile weights by q if we add a box to the height function and the two periodic weighting which exhibits a flat region with defects in the center

correlation function of the schur process with a fixed final partition we consider a generalization of the schur process in which a partition evolves from the empty partition into an arbitrary fixed final partition we obtain a double integral representation of the correlation kernel for a special final partition with only one row the edge scaling limit is also discussed by the use of the saddle point analysis if we appropriately scale the length of the row the limiting correlation kernel changes from the extended airy kernel

arctic curves of the six vertex model on generic domains the tangent method we revisit the problem of determining the arctic curve in the six vertex model with domain wall boundary conditions we describe an alternative method by which we recover the previously conjectured analytic expression in the square domain we adapt the method to work for a large class of domains and for other models exhibiting limit shape phenomena we study in detail some examples and derive in particular the arctic curve of the six vertex model in a triangoloid domain at the ice point

an interactive weighted tchebycheff procedure for multiple objective programming the procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted tchebycheff metric using filtering techniques maximally dispersed representatives of smaller and smaller subsets of the set of nondominated criterion vectors are presented at each iteration the procedure has the advantage that it can converge to non extreme final solutions especially suitable for multiple objective linear programming the procedure is also applicable to integer and nonlinear multiple objective programs

universality for the pearcey process consider non intersecting brownian motions on the line leaving from the origin and forced to two arbitrary points letting the number of brownian particles tend to infinity and upon rescaling there is a point of bifurcation where the support of the density of particles goes from one interval to two intervals in this paper we show that at that very point of bifurcation a cusp appears near which the brownian paths fluctuate like the pearcey process this is a universality result within this class of problems tracy and widom obtained such a result in the symmetric case when the two target points are symmetric with regard to the origin this asymmetry enabled us to improve considerably a result concerning the non linear partial differential equations governing the transition probabilities for the pearcey process obtained by adler and van moerbeke c 2010 elsevier b v all rights reserved

limited information goodness of fit testing in multidimensional contingency tables we introduce a family of goodness of fit statistics for testing composite null hypotheses in multidimensional contingency tables these statistics are quadratic forms in marginal residuals up to order r they are asymptotically chi square under the null hypothesis when parameters are estimated using any asymptotically normal consistent estimator for a widely used item response model when r is small and multidimensional tables are sparse the proposed statistics have accurate empirical type i errors unlike pearson s x2 for this model in nonsparse situations the proposed statistics are also more powerful than x2 in addition the proposed statistics are asymptotically chi square when applied to subtables and can be used for a piecewise goodness of fit assessment to determine the source of misfit in poorly fitting models

pdes for the joint distributions of the dyson airy and sine processes in a celebrated paper dyson shows that the spectrum of an n x n random hermitian matrix diffusing according to an ornstein uhlenbeck process evolves as n noncolliding brownian motions held together by a drift term the universal edge and bulk scalings for hermitian random matrices applied to the dyson process lead to the airy and sine processes in particular the airy process is a continuous stationary process describing the motion of the outermost particle of the dyson brownian motion when the number of particles gets large with space and time appropriately rescaled in this paper we answer a question posed by kurt johansson to find a pde for the joint distribution of the airy process at two different times similarly we find a pde satisfied by the joint distribution of the sine process this hinges on finding a pde for the joint distribution of the dyson process which itself is based on the joint probability of the eigenvalues for coupled gaussian hermitian matrices the pde for the dyson process is then subjected to an asymptotic analysis consistent with the edge and bulk rescalings the pdes enable one to compute the asymptotic behavior of the joint distribution and the correlation for these processes at different times t 1 and t 2 when t 2 t 1 infinity as illustrated in this paper for the airy process this paper also contains a rigorous proof that the extended hermite kernel governing the joint probabilities for the dyson process converges to the extended airy and sine kernels after the appropriate rescalings

discrete orthogonal polynomial ensembles and the plancherel measure we consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory these ensembles occur in certain problems in combinatorial probability and can be thought of as probability measures on partitions the meixner ensemble is related to a two dimensional directed growth model and the charlier ensemble is related to the lengths of weakly increasing subsequences in random words the krawtchouk ensemble occurs in connection with zig zag paths in random domino tilings of the aztec diamond and also in a certain simplifled directed flrst passage percolation model we use the charlier ensemble to investigate the asymptotics of weakly increasing subsequences in random words and to prove a conjecture of tracy and widom as a limit of the meixner ensemble or the charlier ensemble we obtain the plancherel measure on partitions and using this we prove a conjecture of baik deift and johansson that under the plancherel measure the distribution of the lengths of the flrst k rows in the partition appropriately scaled converges to the asymptotic joint distribution for the k largest eigenvalues of a random matrix from the gaussian unitary ensemble in this problem a certain discrete kernel which we call the discrete bessel kernel plays an important role

domino tilings and the six vertex model at its free fermion point at the free fermion point the six vertex model with domain wall boundary conditions dwbc can be related to the aztec diamond a domino tiling problem we study the mapping on the level of complete statistics for general domains and boundary conditions this is obtained by associating with both models a set of non intersecting lines in the lindstrom gessel viennot lgv scheme one of the consequences for dwbc is that the boundaries of the ordered phases are described by the airy process in the thermodynamic limit

domino statistics of the two periodic aztec diamond random domino tilings of the aztec diamond shape exhibit interesting features and some of the statistical properties seen in random matrix theory as a statistical mechanical model it can be thought of as a dimer model or as a certain random surface we consider the aztec diamond with a two periodic weighting which exhibits all three possible phases that occur in these types of models often referred to as solid liquid and gas to analyze this model we use entries of the inverse kasteleyn matrix which give the probability of any configuration of dominoes a formula for these entries for this particular model was derived by chhita and young 2014 in this paper we find a major simplification of this formula expressing entries of the inverse kasteleyn matrix by double contour integrals which makes it possible to investigate their asymptotics in a part of the aztec diamond where the asymptotic analysis is simpler we use this formula to show that the entries of the inverse kasteleyn matrix converge to the known entries of the full plane inverse kasteleyn matrices for the different phases we also study the detailed asymptotics of the inverse kasteleyn matrix at both the liquid solid and liquid gas boundaries and find the extended airy kernel in the next order asymptotics finally we provide a potential candidate for a combinatorial description of the liquid gas boundary

large time asymptotics of growth models on space like paths ii png and parallel tasep we consider the polynuclear growth png model in 1 1 dimension with flat initial condition and no extra constraints the joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a signed determinantal point process the long time scaling limit of the surface height is shown to coincide with the airy1 process this result holds more generally for the observation points located along any space like path in the space time plane we also obtain the corresponding results for the discrete time tasep totally asymmetric simple exclusion process with parallel update

nonintersecting brownian motions on the unit circle we consider an ensemble of n nonintersecting brownian particles on the unit circle with diffusion parameter n 1 2 which are conditioned to begin at the same point and to return to that point after time t but otherwise not to intersect there is a critical value of t which separates the subcritical case in which it is vanishingly unlikely that the particles wrap around the circle and the supercritical case in which particles may wrap around the circle in this paper we show that in the subcritical and critical cases the probability that the total winding number is zero is almost surely 1 as n and in the supercritical case that the distribution of the total winding number converges to the discrete normal distribution we also give a streamlined approach to identifying the pearcey and tacnode processes in scaling limits the formula of the tacnode correlation kernel is new and involves a solution to a lax system for the painleve ii equation of size 2 2 the proofs are based on the determinantal structure of the ensemble asymptotic results for the related system of discrete gaussian orthogonal polynomials and a formulation of the correlation kernel in terms of a double contour integral

formulas for joint probabilities for the asymmetric simple exclusion process in earlier work the authors tracy c a and widom h integral formulas for the asymmetric simple exclusion process commun math phys 279 815 2008 obtained integral formulas for probabilities for a single particle in the asymmetric simple exclusion process here formulas are obtained for joint probabilities for several particles in the case of a single particle the derivation here is simpler than the one in the earlier work for one of its main results

identifiability and equivalence of gllirm models the generalized logit linear item response model gllirm is a linearly constrained nominal categories model ncm that computes the scale and intercept parameters for categories as a weighted sum of basic parameters this paper addresses the problems of the identifiability of the basic parameters and the equivalence between different gllirm models it is shown that the identifiability of the basic parameters depends on the size and rank of the coefficient matrix of the linear functions moreover two models are observationally equivalent if the product of the respective coefficient matrices has full column rank finally the paper also explores the relations between the parameters of nested models

multidimensional cat item selection methods for domain scores and composite scores theory and applications multidimensional computer adaptive testing mcat can provide higher precision and reliability or reduce test length when compared with unidimensional cat or with the paper and pencil test this study compared five item selection procedures in the mcat framework for both domain scores and overall scores through simulation by varying the structure of item pools the population distribution of the simulees the number of items selected and the content area the existing procedures such as volume segall in psychometrika 61 331 354 1996 kullback leibler information veldkamp van der linden in psychometrika 67 575 588 2002 minimize the error variance of the linear combination van der linden in j educ behav stat 24 398 412 1999 and minimum angle reckase in multidimensional item response theory springer new york 2009 are compared to a new procedure minimize the error variance of the composite score with the optimized weight proposed for the first time in this study the intent is to find an item selection procedure that yields higher precisions for both the domain and composite abilities and a higher percentage of selected items from the item pool the comparison is performed by examining the absolute bias correlation test reliability time used and item usage three sets of item pools are used with the item parameters estimated from real live cat data results show that volume and minimum angle performed similarly balancing information for all content areas while the other three procedures performed similarly with a high precision for both domain and overall scores when selecting items with the required number of items for each domain the new item selection procedure has the highest percentage of item usage moreover for the overall score it produces similar or even better results compared to those from the method that selects items favoring the general dimension using the general model segall in psychometrika 66 79 97 2001 the general dimension method has low precision for the domain scores in addition to the simulation study the mathematical theories for certain procedures are derived the theories are confirmed by the simulation applications

a primogenitary linked quad tree approach for solution storage and retrieval in heuristic binary optimization abstract a data structure called the primogenitary linked quad tree plqt is used to store and retrieve solutions in heuristic solution procedures for binary optimization problems two ways are proposed to use integer vectors to represent solutions represented by binary vectors one way is to encode binary vectors into integer vectors in a much lower dimension and the other is to use the sorted indices of binary variables with values equal to 0 or equal to 1 the integer vectors are used as composite keys to store and retrieve solutions in the plqt an algorithm processing trial solutions for insertion into or retrieval from the plqt is developed examples are provided to demonstrate the way the algorithm works another algorithm traversing the plqt is also developed computational results show that the plqt approach takes only a very tiny portion of the cpu time taken by a linear list approach for the same purpose for any reasonable application the cpu time taken by the plqt managing trial solutions is negligible as compared to that taken by a heuristic procedure for any reasonably hard to solve binary optimization problem as shown in a tabu search heuristic procedure for the capacitated facility location problem compared to the hashing approach the plqt approach takes the same or less amount of cpu time but much less memory space while completely eliminating collision

stochastic higher spin six vertex model and macdonald measures we prove an identity that relates the q laplace transform of the height function of a higher spin inhomogeneous stochastic six vertex model in a quadrant on one side and a multiplicative functional of a macdonald measure on the other the identity is used to prove the gue tracy widom asymptotics for two instances of the stochastic six vertex model via asymptotic analysis of the corresponding schur measures