a note on the regression analysis of censored data maximum likelihood estimates of the parameters in linear models with censored normal responses may be simply obtained using the em algorithm the iterative computations required for the regression coefficients are identical to those described by schmee and hahn for least squares estimates but those for the variance estimates are different the biases of the two variance estimates are discussed

the analysis of a fractional factorial experiment with censored data using iterative least squares schmee and hahn 1979 suggested iterative least squares as a simple method for analyzing censored data the application of this method to the analysis of the results of a fractional factorial experiment with censored observations is described and illustrated in this paper

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

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

height fluctuations in the honeycomb dimer model we study a model of random surfaces arising in the dimer model on the honeycomb lattice for a fixed wire frame boundary condition as the lattice spacing 0 cohn kenyon and propp 3 showed the almost sure convergence of a random surface to a non random limit shape 0 in 12 okounkov and the author showed how to parametrize the limit shapes in terms of analytic functions in particular constructing a natural conformal structure on them we show here that when 0 has no facets for a family of boundary conditions approximating the wire frame the large scale surface fluctuations height fluctuations about 0 converge as 0 to a gaussian free field for the above conformal structure we also show that the local statistics of the fluctuations near a given point x are as conjectured in 3 given by the unique ergodic gibbs measure on plane configurations whose slope is the slope of the tangent plane of 0 at x

shuffling algorithm for boxed plane partitions we introduce discrete time markov chains that preserve uniform measures on boxed plane partitions elementary markov steps change the size of the box from a b c to a 1 b 1 c or a 1 b 1 c algorithmic realization of each step involves o a b c operations one application is an efficient perfect random sampling algorithm for uniformly distributed boxed plane partitions trajectories of our markov chains can be viewed as random point configurations in the three dimensional lattice we compute the bulk limits of the correlation functions of the resulting random point process on suitable two dimensional sections the limiting correlation functions define a two dimensional determinantal point processes with certain gibbs properties

local limits of lozenge tilings are stable under bounded boundary height perturbations we show that bounded changes to the boundary of a lozenge tilings do not affect the local behaviour inside the domain as a consequence we prove the existence of a local limit in all domains with planar boundary the proof does not rely on any exact solvability of the model beyond its links with uniform spanning trees

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

thermodynamic limit of random partitions and dispersionless toda hierarchy we study the thermodynamic limit of random partition models for the instanton sum of 4d and 5d supersymmetric u 1 gauge theories deformed by some physical observables the physical observables correspond to external potentials in the statistical model the partition function is reformulated in terms of the density function of maya diagrams the thermodynamic limit is governed by a limit shape of young diagrams associated with dominant terms in the partition function the limit shape is characterized by a variational problem which is further converted to a scalar valued riemann hilbert problem this riemann hilbert problem is solved with the aid of a complex curve which may be thought of as the seiberg witten curve of the deformed u 1 gauge theory this solution of the riemann hilbert problem is identified with a special solution of the dispersionless toda hierarchy that satisfies a pair of generalized string equations the generalized string equations for the 5d gauge theory are shown to be related to hidden symmetries of the statistical model the prepotential and the seiberg witten differential are also considered

analysis of censored data from fractionated experiments a bayesian approach abstract censored data arise naturally in industrial experiments whose observations are failure times or measurements with mixed continuous categorical outcomes when censored data are observed from a fractionated experiment likelihood based estimates quite often do not exist especially when the opportunity for improvement is great to circumvent this problem we propose a bayesian analysis strategy that has a straightforward implementation using the data augmentation and monte carlo em algorithms for nonregular designs with complex aliasing patterns a modified analysis strategy is proposed that substantially reduces the computation needed for model selection the proposed strategy is illustrated using data from three real industrial experiments for these data sets the analysis results are fairly insensitive to the specification of the prior

alternating subspace spanning resampling to accelerate markov chain monte carlo simulation this article provides a simple method to accelerate markov chain monte carlo sampling algorithms such as the data augmentation algorithm and the gibbs sampler via alternating subspace spanning resampling assr the assr algorithm often shares the simplicity of its parent sampler but has dramatically improved efficiency the methodology is illustrated with bayesian estimation for analysis of censored data from fractionated experiments the relationships between assr and existing methods are also discussed

lozenge tilings and hurwitz numbers we give a new proof of the fact that near a turning point of the frozen boundary the vertical tiles in a uniformly random lozenge tiling of a large sawtooth domain are distributed like the eigenvalues of a gue random matrix our argument uses none of the standard tools of integrable probability in their place it uses a combinatorial interpretation of the harish chandra itzykson zuber integral as a generating function for desymmetrized hurwitz numbers

analysis of interval censored data from fractionated experiments using covariance adjustment censored data are commonly observed in industrial experiments such as for life testing and reliability improvement analyzing censored data from highly fractionated experiments presents a challenging problem to experimenters because many traditional methods become inadequate motivated by the data from a fluorescent lamp experiment we consider in this article analyzing censored data from highly fractionated experiments using covariance adjustment based on multivariate multiple regression models which make use of the joint distribution of multivariate response variables the bayesian approach is taken for the main statistical inference the posterior distribution of the parameters is obtained using the data augmentation algorithm we illustrate the methodology with the fluorescent lamp experiment data with the real example and a simulation study we show that covariance adjustment can lead to both dramatic variance reduction and possible bias reduction

asymptotics of uniformly random lozenge tilings of polygons gaussian free field we study large scale height fluctuations of random stepped surfaces corresponding to uniformly random lozenge tilings of polygons on the triangular lattice for a class of polygons which allows arbitrarily large number of sides we show that these fluctuations are asymptotically governed by a gaussian free massless field this complements the similar result obtained in kenyon comm math phys 281 2008 675 709 about tilings of regions without frozen facets of the limit shape in our asymptotic analysis we use the explicit double contour integral formula for the determinantal correlation kernel of the model obtained previously in petrov asymptotics of random lozenge tilings via gelfand tsetlin schemes 2012 preprint

tools for template dependencies template dependencies td s are a class of data dependencies that include multivalued and join dependencies and embedded versions of these a collection of techniques examples and results about td s are presented the principal results are 1 finite implication implication over relations with a finite number of tuples is distinct from unrestricted implication for td s 2 there are for td s over three or more attributes infinite chains of increasingly weaker and increasingly stronger full td s 3 however there are weakest nontrivial and strongest full td s over any given set of attributes 4 over two attributes there are only three distinct td s 5 there is no weakest not necessarily full td over any set of three or more attributes 6 there is a finite relation that obeys every strictly partial td but no full td 7 the conjunction of each finite set of full td s is equivalent to a single full td however the conjunction of a finite set of not necessarily full td s is not necessarily e

reasoning about functional and full hierarchical dependencies over partial relations we study the implication problem for the combined class of functional and full hierarchical dependencies in the presence of sql s not null constraints two different notions of implication are addressed one where a dependency is implied by the given set of dependencies plus the underlying schema and one where a dependency is implied by the given set of dependencies alone we establish axiomatizations for both notions of implication and reveal deep relationships between them

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

the low temperature expansion of the wulff crystal in the 3d ising model we compute the expansion of the surface tension of the 3d random cluster model for q 1 in the limit where p goes to 1 we also compute the asymptotic shape of a plane partition of n as n goes to this same shape determines the wulff crystal to order o in the 3d ising model and more generally in the 3d random cluster model for q 1 at temperature

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

bulk universality for random lozenge tilings near straight boundaries and for tensor products we prove that the asymptotic of the bulk local statistics in models of random lozenge tilings is universal in the vicinity of straight boundaries of the tiled domains the result applies to uniformly random lozenge tilings of large polygonal domains on triangular lattice and to the probability measures describing the decomposition in gelfand tsetlin bases of tensor products of representations of unitary groups in a weaker form our theorem also applies to random domino tilings

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

an application of imputation to an estimation problem in grouped lifetime analysis tanner and wang in press have introduced the data augmentation algorithm for the analysis of parametric missing data problems in this article this paradigm is used to develop an algorithm for the nonparametric estimation of the hazard function from grouped and censored lifetime data this algorithm makes use of the notions of cross validation and multiple imputation to prescribe the appropriate degree of smoothing for the nonparametric hazard estimate a procedure for estimating the variance of the estimator is also proposed the nonparametric hazard estimate and corresponding variance formula are shown to perform well in a simulation study the algorithm is illustrated with a numerical example

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

asymptotics of random lozenge tilings via gelfand tsetlin schemes a gelfand tsetlin scheme of depth n is a triangular array with m integers at level m m 1 ldots n subject to certain interlacing constraints we study the ensemble of uniformly random gelfand tsetlin schemes with arbitrary fixed n th row we obtain an explicit double contour integral expression for the determinantal correlation kernel of this ensemble and also of its q deformation this provides new tools for asymptotic analysis of uniformly random lozenge tilings of polygons on the triangular lattice or equivalently of random stepped surfaces we work with a class of polygons which allows arbitrarily large number of sides we show that the local limit behavior of random tilings as all dimensions of the polygon grow is directed by ergodic translation invariant gibbs measures the slopes of these measures coincide with the ones of tangent planes to the corresponding limit shapes described by kenyon and okounkov acta math 199 2 263 302 2007 we also prove that at the edge of the limit shape the asymptotic behavior of random tilings is given by the airy process in particular our results cover the most investigated case of random boxed plane partitions when the polygon is a hexagon

membership problem for embedded multivalued dependencies under some restricted conditions abstract it is known that there is no finite set of inference rules that is complete for embedded multivalued dependencies this paper considers the problem called membership problem of deciding whether a given embedded multivalued dependency x v on u or functional dependency x v is implied by a given set d of functional and embedded multivalued dependencies a new inference rule for embedded multivalued dependencies is presented and the following results about membership problems are shown let u be a set of attributes and let w n w 0 u let d f e e 1 e n where 1 i f is a set of functional dependencies y z satisfying y w 0 or z w 0 2 ii e is a set of embedded multivalued dependencies y z on t satisfying at least one of y w 0 t z w 0 and t y z w 0 and 3 iii each e 1 i n is a set of embedded multivalued dependencies on w 1 1 if x v u w 0 then the membership problem is solaable that is it is decidable whether x v on u or x v is implied by d 2 2 if x v u w n then the membership problem cah be solved in o d v x time where d is the size of the description of d 3 3 if x w n and x v u w 0 then the membership problem can be solved in o d 2 w n x n t 1 w 1 w 1 l 1 time

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

analysis of censored data from highly fractionated experiments although censored including interval censored data may be easier or less costly to collect than complete data they contain less information and are harder to analyze existing methodology is inadequate for analyzing such data from highly fractionated experiments we propose an iterative method that provides a simple and flexible way to consider many models simultaneously the method s simplicity makes it easy to implement with existing software results in computational savings and promotes experimenter involvement we demonstrate the procedure by reanalyzing data from two real experiments a simulation study also demonstrates its superiority over some existing methods including taguchi s minute accumulating analysis

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

an equivalence between relational database dependencies and a fragment of propositional logic it is known that there is an eqmvalence between functional dependencies m a relatmonal database and a certain fragment of proposmonal logic thins eqmvalence is extended to include both functional and multivalued dependencmes thus for each dependency there is a corresponding statement m proposmonal logic it ms then shown that a dependency funcuonal or multivalued is a consequence of a set of dependencies ff and only ff the corresponding proposiuonal statement s a consequence of the corresponding set of proposmonal statements examples are given to show that these techniques are valuable mn provmdmg much shorter proofs of theorems about dependencies than have been obtained by more tradmonal means it is shown that this eqmvalence cannot be extended to include either join dependencies or embedded multmvalued dependencies

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

dimers and amoebae we study random surfaces which arise as height functions of random perfect matchings a k a dimer configurations on a weighted bipartite doubly periodic graph g embedded in the plane we derive explicit formulas for the surface tension and local gibbs measure probabilities of these models the answers involve a certain plane algebraic curve which is the spectral curve of the kasteleyn operator of the graph for example the surface tension is the legendre dual of the ronkin function of the spectral curve the amoeba of the spectral curve represents the phase diagram of the dimer model further we prove that the spectral curve of a dimer model is always a real curve of special type namely it is a harnack curve this implies many qualitative and quantitative statement about the behavior of the dimer model such as existence of smooth phases decay rate of correlations growth rate of height function fluctuations etc

a proof procedure for data dependencies definition d une classe de dependances dependances generant l equalite et les triples et generalisation du processus de poursuite pour traiter ces dependances on montre quelques cas pour lesquels il y a une procedure de decision redondance de l egalite pour decider de l implication des dependances generant les triples et presque redondance pour decider de l implication des dependances generant l egalite

some aspects of analysis of covariance an account from first principles is given of a number of aspects of analysis of covariance six different meanings of analysis of covariance are outlined and the history of this technique is sketched briefly the development of the key formulae from the method of least squares is described and generalizations to other distributions in the exponential family are mentioned special problems of application in randomized experiments and in observational studies are discussed finally the decomposition of regression relations is considered along with components of covariance

sort sets in the relational model the notion of sort set is introduced here to formalize the fact that certain database relations can be sorted so that two or more columns are simultaneously listed in order this notion is shown to be applicable in several ways to enhance the efficiency of an implemented database a characterization of when order dependency implies the existence of sort sets in a database is presented along with several corollaries concerning complexity armstrong relations and cliques of certain graphs sort set dependencies are then introduced a finite sound and complete set of inference rules for sort set dependencies is presented as well as a proof that there is no such set for functional and sort set dependencies taken together deciding logical implication for sort set dependencies is proved to be polynomial but if functional dependencies are included the problem is co np complete each set of sort set and functional dependencies is shown to have an armstrong relation a natural generalization of armstrong relation here called separator is given and then used to study the relationship between order and sort set dependencies

log gases on quadratic lattices via discrete loop equations and q boxed plane partitions abstract we study a general class of log gas ensembles on shifted quadratic lattices we prove that the corresponding empirical measures satisfy a law of large numbers and that their global fluctuations are gaussian with a universal covariance we apply our general results to analyze the asymptotic behavior of a q boxed plane partition model introduced by borodin gorin and rains in particular we show that the global fluctuations of the height function on a fixed slice are described by a one dimensional section of a pullback of the two dimensional gaussian free field our approach is based on a q analogue of the schwinger dyson or loop equations which originate in the work of nekrasov and his collaborators and extends the methods developed by borodin gorin and guionnet to quadratic lattices

functional dependencies and constraints on null values in database relations database relations with incomplete information are considered the no information interpretation of null values is adopted due to its characteristics of generality and naturalness coherently with the framework and its motivation two meaningful classes of integrity constraints are studied a functional dependencies which have been widely investigated in the classical relational theory and b constraints on null values which control the presence of nulls in the relations specifically three types of constraints on null values are taken into account nullfree subschemes existence constraints disjunctive existence constraints and the interaction of each of them with functional dependencies is studied in each of the three cases the inference problem is solved the complexity of the algorithms for its solution analyzed and the existence of a complete axiomatization discussed

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

addition of certain non commuting random variables soit g le groupe libre non commutatif sur deux generateurs et soit u j j 1 2 les unites dans l 2 g correspondant a la translation a gauche par les generateurs et on considere l 2 g la fonction g g e soient x j des operateurs de la forme x j j u j les operateurs x j peuvent etre consideres comme des variables aleatoires de moments ou de facon equivalente avec des distributions donnees par les fonctionnelles analytiques j ou j f avec ces conventions la distribution de x 1 x 2 depend seulement des distributions de x 1 et x 2 on explique cette relation

on the undecidability of implications between embedded multivalued database dependencies the implication and finite implication problems for embedded multivalued database dependencies are both shown to be algorithmically undecidable the proof is by an interpretation of semigroup word problems via systems of permuting equivalence relations into database dependencies in contrast it is shown that for each fixed premise h one has a decision procedure for implications h f

limit shapes and the complex burgers equation in this paper we study surfaces in r 3 that arise as limit shapes in random surface models related to planar dimers these limit shapes are surface tension minimizers that is they minimize a functional of the form h dx dy among all lipschitz functions h taking given values on the boundary of the domain the surface tension has singularities and is not strictly convex which leads to formation of facets and edges in the limit shapes we find a change of variables that reduces the euler lagrange equation for the variational problem to the complex inviscid burgers equation complex hopf equation the equation can thus be solved in terms of an arbitrary holomorphic function which is somewhat similar in spirit to weierstrass parametrization of minimal surfaces we further show that for a natural dense set of boundary conditions the holomorphic function in question is in fact algebraic the tools of algebraic geometry can thus be brought in to study the minimizers and especially the formation of their singularities this is illustrated by several explicitly computed examples

inferences for numerical dependencies abstract we introduce and motivate the study of numerical dependencies which are a generalization of functional dependencies we prove that there does not exist a finite set of sound and complete inference rules for numerical dependencies in contrast to the case of functional dependencies we also prove that nontrivial numerical dependencies which are not functional dependencies cannot be expressed by horn formulas in first order logic and show some applications of numerical dependencies

the quasi invariance property for the gamma kernel determinantal measure abstract the gamma kernel is a projection kernel of the form a x b y b x a y x y where a and b are certain functions on the one dimensional lattice expressed through euler s function the gamma kernel depends on two continuous parameters its principal minors serve as the correlation functions of a determinantal probability measure p defined on the space of infinite point configurations on the lattice as was shown earlier a borodin g olshanski adv math 194 2005 141 202 arxiv math ph 0305043 p describes the asymptotics of certain ensembles of random partitions in a limit regime theorem the determinantal measure p is quasi invariant with respect to finitary permutations of the nodes of the lattice this result is motivated by an application to a model of infinite particle stochastic dynamics

axioms and algorithms for inferences involving probabilistic independence abstract this paper offers an axiomatic characterization of the probabilistic relation x is independent of y written x y where x and y are two disjoint sets of variables four axioms for x y are presented and shown to be complete based on these axioms a polynomial membership algorithm is developed to decide whether any given independence statement x y logically follows from a set of such statements i e whether x y holds in every probability distribution that satisfies the complexity of the algorithm is o k2 n where is the number of given statements n is the number of variables in x y and k is the number of variables in x y

bayesian analysis of systems of seemingly unrelated regression equations under a recursive extended natural conjugate prior density abstract a recursive extended natural conjugate prior density is proposed for systems of seemingly unrelated regression equations compared to other classes of extended natural conjugate prior densities it offers the advantage that analytical expressions are available for the prior covariance matrix of the regression coefficients the posterior analysis combines analytical and numerical techniques numerical integration is based on monte carlo importance sampling an application to a system of four wage equations for eec countries serves to evaluate different techniques discussed in the paper

differential equations for dyson processes we call a dyson process any process on ensembles of matrices in which the entries undergo diffusion we are interested in the distribution of the eigenvalues or singular values of such matrices in the original dyson process it was the ensemble of n n hermitian matrices and the eigenvalues describe n curves given sets x1 xm the probability that for each k no curve passes through xk at time k is given by the fredholm determinant of a certain matrix kernel the extended hermite kernel for this reason we call this dyson process the hermite process similarly when the entries of a complex matrix undergo diffusion we call the evolution of its singular values the laguerre process for which there is a corresponding extended laguerre kernel scaling the hermite process at the edge leads to the airy process which was introduced by prahofer and spohn as the limiting stationary process for a polynuclear growth model and in the bulk to the sine process scaling the laguerre process at the edge leads to the bessel process

asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory we develop a new method for studying the asymptotics of symmetric polynomials of representation theoretic origin as the number of variables tends to infinity several applications of our method are presented we prove a number of theorems concerning characters of infinite dimensional unitary group and their q deformations we study the behavior of uniformly random lozenge tilings of large polygonal domains and find the gue eigenvalues distribution in the limit we also investigate similar behavior for alternating sign matrices equivalently six vertex model with domain wall boundary conditions finally we compute the asymptotic expansion of certain observables in theo n 1 dense loop model

fluctuations of particle systems determined by schur generating functions abstract we develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems we introduce and study the notion of the schur generating function of a random discrete configuration our main result provides a central limit theorem clt for such a configuration given certain conditions on the schur generating function as applications of this approach we prove clt s for several probabilistic models coming from asymptotic representation theory and statistical physics including random lozenge and domino tilings non intersecting random walks decompositions of tensor products of representations of unitary groups

universality of the local spacing distribution in certain ensembles of hermitian wigner matrices consider an n n hermitian random matrix with independent entries not necessarily gaussian a so called wigner matrix it has been conjectured that the local spacing distribution i e the distribution of the distance between nearest neighbour eigenvalues in some part of the spectrum is in the limit as n the same as that of hermitian random matrices from gue we prove this conjecture for a certain subclass of hermitian wigner matrices

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

asymptotics of plancherel measures for symmetric groups 1 1 plancherel measures given a finite group g by the corresponding plancherel measure we mean the probability measure on the set g of irreducible representations of g which assigns to a representation g the weight dim g for the symmetric group s n the set s n is the set of partitions of the number n which we shall identify with young diagrams with n squares throughout this paper the plancherel measure on partitions arises naturally in representation theoretic combinatorial and probabilistic problems for example the plancherel distribution of the first part of a partition coincides with the distribution of the longest increasing subsequence of a uniformly distributed random permutation 31 we denote the plancherel measure on partitions of n by mn

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea