directed walks and vertex models renormalization multicriticality and beyond we discuss the exact renormalization of interacting directed random walks drw using dimensional regularization and the exact results for the multicritical points we discuss how these exact results of the drw problem can give exact critical exponents ofthe ferroelectric five vertex model in all dimensions the multicritical drw s lead to a new class of vertex models whose multicritical exponents can be computed exactly a random vertex model and its connection to the drw problem in a random medium is also discussed

on the convergence of diffusion processes conditioned to remain in a bounded region for large time to limiting positive recurrent diffusion processes let x t be a diffusion process on r d with generator l 1 2 nabla cdot a nabla b nabla and let p x x in r d be the corresponding measures on paths pick 0 s which are always satisfied if a 1 b is a gradient function we show that y t s is an inhomogeneous diffusion process and that as t rightarrow infty y t s 0 leq s leq t converges to a limiting homogeneous positive recurrent diffusion y s 0 leq s leq t with state space g since t is arbitrary we actually obtain a limiting process y s 0 leq s infty the generator of the limiting process may be written in the form l g 1 2 nabla cdot a nabla b nabla a nabla g 0 g 0 nabla a nabla h g 0 nabla where g 0 is the square root of the density of a measure mu 0 which minimizes the i function for the process over all gamma in mathscr p bar g the set of probability measures on bar g the function h g 0 appears in the explicit calculation of i mu 0 and solves a certain variational equation the invariant measure for the process is mu 0

component selection and smoothing in multivariate nonparametric regression we propose a new method for model selection and model fitting in multivariate nonparametric regression models in the framework of smoothing spline anova the cosso is a method of regularization with the penalty functional being the sum of component norms instead of the squared norm employed in the traditional smoothing spline method the cosso provides a unified framework for several recent proposals for model selection in linear models and smoothing spline anova models theoretical properties such as the existence and the rate of convergence of the cosso estimator are studied in the special case of a tensor product design with periodic functions a detailed analysis reveals that the cosso does model selection by applying a novel soft thresholding type operation to the function components we give an equivalent formulation of the cosso estimator which leads naturally to an iterative algorithm we compare the cosso with mars a popular method that builds functional anova models in simulations and real examples the cosso method can be extended to classification problems and we compare its performance with those of a number of machine learning algorithms on real datasets the cosso gives very competitive performance in these studies

cyclic plasticity using prager s translation rule and both nonlinear kinematic and isotropic hardening theory validation and algorithmic implementation abstract finite element analysis of structures under elasto plastic nonproportional cyclic loadings is useful in seismic engineering fatigue analysis and ductile fracture usual models with nonlinear stress strain curves in cyclic behavior are based on mroz multisurface plasticity bounding surface models or models derived from the armstrong frederick rule these models depart from the associative prager s rule with the main purpose of modeling aspects of cyclic nonlinear hardening in this paper we develop a model for cyclic plasticity within the framework of the associative classical plasticity theory using prager s rule accounting for anisotropic nonlinear kinematic hardening coupled with nonlinear isotropic hardening we include the validation of the theory against several uniaxial and multiaxial cyclic experiments and an efficient fully implicit radial return algorithm the parameters of the model are obtained directly by a discretization of the uniaxial stress strain behavior remarkably both the presented theory and the computational algorithm automatically recover classical bi linear plasticity and the krieg and key algorithm if the user prescribed stress strain curve is bilinear

correlation functions cluster functions and spacing distributions for random matrices the usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants from this representation one can deduce formulas for spacing probabilities in terms of fredholm determinants of matrix valued kernels the derivations of the various formulas are somewhat involved in this article we present a direct approach which leads immediately to scalar kernels for the unitary ensembles and matrix kernels for the orthogonal and symplectic ensembles and the representations of the correlation functions cluster functions and spacing distributions in terms of them

conformal invariance of domino tiling let u be a multiply connected region in r 2 with smooth boundary let p be a polyomino in z 2 approximating u as 0 we show that for certain boundary conditions on p the height distribution on a random domino tiling dimer covering of p is conformally invariant in the limit as tends to 0 in the sense that the distribution of heights of boundary components or rather the difference of the heights from their mean values only depends on the conformal type of u the mean height is not strictly conformally invariant but transforms analytically under conformal mappings in a simple way the mean height and all the moments are explicitly evaluated

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

smoothing spline gaussian regression more scalable computation via efficient approximation summary smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with gaussian responses the computation of smoothing splines is generally of the order o n3 n being the sample size which severely limits its practical applicability we study more scalable computation of smoothing spline regression via certain low dimensional approximations that are asymptotically as efficient a simple algorithm is presented and the bayes model that is associated with the approximations is derived with the latter guiding the porting of bayesian confidence intervals the practical choice of the dimension of the approximating space is determined through simulation studies and empirical comparisons of the approximations with the exact solution are presented also evaluated is a simple modification of the generalized cross validation method for smoothing parameter selection which to a large extent fixes the occasional undersmoothing problem that is suffered by generalized cross validation

exact results for vicious walker models of domain walls non intersecting or vicious random walker models in one dimension can be interpreted as models of domain walls in two dimensions three problems pertaining to vicious walker models are solved the first is the exact evaluation of the partition function for the random turns model of vicious walkers on a lattice in this model at each tick of the clock a randomly chosen walker must move one step to the left or one step to the right the second problem is the calculation of the mean spacing between walls in terms of the chemical potential for a brownian motion model of continuous domain walls in a strip while the final problem solved is the calculation of the correlation between defects which occur when two domain walls meet and end without crossing the whole system

anisotropic self avoiding walks we consider a model of self avoiding walks on the lattice zd with different weights for steps in each of the 2d lattice directions we find that the direction dependent mass for the two point function of this model has three phases mass positive in all directions mass identically and masses of different signs in different directions the final possibility can only occur if the weights are asymmetric i e in at least one coordinate the weight in the positive direction differs from the weight in the negative direction the boundaries of these phases are determined exactly we also prove that if the weights are asymmetric then a typical n step self avoiding walk has order n distance between its endpoints

vertex models and directed walks length scale exponents from finite size scaling by using the mapping between ferroelectric five vertex or the modified kdp model and directed walks the authors prove via finite size scaling that the length scale exponents nu sub and nu perpendicular to are related by nu sub 2 nu perpendicular to in all dimensions

more efficient approximation of smoothing splines via space filling basis selection we consider the problem of approximating smoothing spline estimators in a nonparametric regression model when applied to a sample of size formula see text the smoothing spline estimator can be expressed as a linear combination of formula see text basis functions requiring formula see text computational time when the number formula see text of predictors is two or more such a sizeable computational cost hinders the broad applicability of smoothing splines in practice the full sample smoothing spline estimator can be approximated by an estimator based on formula see text randomly selected basis functions resulting in a computational cost of formula see text it is known that these two estimators converge at the same rate when formula see text is of order formula see text where formula see text depends on the true function and formula see text depends on the type of spline such a formula see text is called the essential number of basis functions in this article we develop a more efficient basis selection method by selecting basis functions corresponding to approximately equally spaced observations the proposed method chooses a set of basis functions with great diversity the asymptotic analysis shows that the proposed smoothing spline estimator can decrease formula see text to around formula see text when formula see text applications to synthetic and real world datasets show that the proposed method leads to a smaller prediction error than other basis selection methods

random walks and random fixed point free involutions a bijection is given between fixed point free involutions of 1 2 2n with maximum decreasing subsequence size 2p and two classes of vicious non intersecting random walker configurations confined to the half line lattice points l 1 in one class of walker configurations the maximum displacement of the rightmost walker is p because the scaled distribution of the maximum decreasing subsequence size is known to be in the soft edge goe random real symmetric matrices universality class the same holds true for the scaled distribution of the maximum displacement of the rightmost walker

dimers belonging to three orientations on plane honeycomb lattices it is well known that there are three types of dimers belonging to the three different orientations in a honeycomb lattice and in each type all dimers are mutually parallel based on a previous result we can compute the partition function of the dimer problem of the plane free boundary honeycomb lattices with three different activities by using the number of its pure dimer coverings perfect matchings the explicit expression of the partition function and free energy per dimer for many types of plane honeycomb lattices with fixed shape of boundaries is obtained in this way for a shape of plane honeycomb lattices the procedure that the size goes to infinite corresponds to a way that the honeycomb lattice goes to infinite from these results an interesting phenomena is observed in the case of the regions of the plane honeycomb lattice has zero entropy per dimer when its size goes to infinite though in the thermodynamic limit there is no freedom in placing a dimer at all but if we distinguish three types of dimers with nonzero activities then its free energy per dimer is nonzero furthermore a sufficient condition for the plane honeycomb lattice with zero entropy per dimer when the three activities are equal to 1 is obtained finally the difference between the plane honeycomb lattices and the plane quadratic lattices is discussed and a related problem is proposed

critical behaviour of self avoiding walks that cross a square consider the set of all self avoiding walks in the square lattice which start at 0 0 end at l l and are entirely contained in the square 0 l 0 l associate a fugacity x with each step of the walk whittington and guttmann 1990 showed that the dominant walks have o l steps when x is small and o l2 steps when x is large and they conjectured that there is a single transition point at x mu 1 where mu is the inverse of the connective constant for unconstrained self avoiding walks we present a rigorous proof of this conjecture and its analogue in higher dimensions we also discuss what can be said rigorously about two scaling exponents associated with this phase transition and compare this with analogous results that have been obtained exactly and rigorously on the discrete sierpinski gasket by hattori hattori and kusuoka 1990

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

on the distribution of the length of the longest increasing subsequence of random permutations let sn be the group of permutations of 1 2 n if 7r e sn we say that 7 i1 7f ik is an increasing subsequence in 7r if il i2 ik and 7r ii 7r i2 7r ik let 1n r be the length of the longest increasing subsequence for example if n 5 and 7r is the permutation 5 1 3 2 4 in one line notation thus 7r 1 5 7r 2 1 then the longest increasing subsequences are 1 2 4 and 1 3 4 and n 3 equip sn with uniform distribution

binomial determinants paths and hook length formulae abstract we give a combinatorial interpretation for any minor or binomial determinant of the matrix of binomial coefficients this interpretation involves configurations of nonintersecting paths and is related to young tableaux and hook length formulae

variable selection and model building via likelihood basis pursuit this article presents a nonparametric penalized likelihood approach for variable selection and model building called likelihood basis pursuit lbp in the setting of a tensor product reproducing kernel hilbert space we decompose the log likelihood into the sum of different functional components such as main effects and interactions with each component represented by appropriate basis functions basis functions are chosen to be compatible with variable selection and model building in the context of a smoothing spline anova model basis pursuit is applied to obtain the optimal decomposition in terms of having the smallest l1 norm on the coefficients we use the functional l1 norm to measure the importance of each component and determine the threshold value by a sequential monte carlo bootstrap test algorithm as a generalized lasso type method lbp produces shrinkage estimates for the coefficients which greatly facilitates the variable selection process and provides highly interpretable multivariate

random vicious walks and random matrices a lock step walk is a one dimensional integer lattice walk in discrete time suppose that initially there are infinitely many walkers on the nonnegative even integer sites at each moment of time every walker moves either to its left or to its right with equal probability the only constraint is that no two walkers can occupy the same site at the same time hence we describe the walk as vicious it is proved that as time tends to infinity a certain limiting conditional distribution of the displacement of the leftmost walker is identical to the limiting distribution of the scaled largest eigenvalue of a random goe matrix goe tracy widom distribution the proof is based on the bijection between path configurations and semistandard young tableaux established recently by guttmann owczarek and viennot the distribution of semistandard young tableaux is analyzed using the hankel determinant expression for the probability obtained from the work of rains and the author the asymptotics of the hankel determinant are then obtained by applying the deift zhou steepest descent method to the riemann hilbert problem for the related orthogonal polynomials 2000 john wiley sons inc

limit theorems for height fluctuations in a class of discrete space and time growth models we introduce a class of one dimensional discrete space discrete time stochastic growth models described by a height function ht x with corner initialization we prove with one exception that the limiting distribution function of ht x suitably centered and normalized equals a fredholm determinant previously encountered in random matrix theory in particular in the universal regime of large x and large t the limiting distribution is the fredholm determinant with airy kernel in the exceptional case called the critical regime the limiting distribution seems not to have previously occurred the proofs use the dual rsk algorithm gessel s theorem the borodin okounkov identity and a novel rigorous saddle point analysis in the fixed x large t regime we find a brownian motion representation this model is equilvalent to the seppalainen johansson model hence some of our results are not new but the proofs are

reconcile the perfectly elastoplastic model to simulate the cyclic behavior and ratcheting perfectly elastoplastic constitutive model is modified through a smoothing factor introduced by liu liu c s 2003 smoothing elastoplastic stress strain curves obtained by a critical modification of conventional models int j solids struct 40 2121 2145 the new model allows plasticity to happen in a non zero measure yield volume in stress space rather than that of conventional zero measure yield surface and within the yield volume the plastic modulus is varying continuously it endows a specific strain hardening rule of flow stress and is able to describe the phenomena of strain hardening cyclic hardening the bauschinger effect mean stress relaxation strain ratcheting out of phase hardening as well as erasure of memory in order to suppress the over prediction of ratcheting we consider a scalar function of smoothing factor which can simulate the saturation behavior of uniaxial multiaxial strain ratcheting these effects are demonstrated through numerical examples the existence of stress equilibrium point and limiting surface is a natural result without requiring an extra design moreover the non linear constitutive equations can be converted into a linear system for augmented stress in the minkowski space of which the symmetry group is a proper orthochronous lorentz group soo 5 1 the augmented stress is a time like vector moving on hyperboloids inside the cone when taking the prager kinematic hardening rule into account we can simulate some cyclic behaviors of sae 4340 and grade 60 steels within a certain accuracy through the use of only three material constants and a fixed smoothing factor to simulate the ratcheting behaviors of ss304 stainless steel we allow the smoothing factor to be an exponential decaying function of k 2005 elsevier ltd all rights reserved

on the consistency of nested surfaces models and their kinematic hardening rules abstract in this paper we briefly address the consistency of formulations for nested surfaces plasticity and their kinematic hardening translation rules some requirements for these formulations are then given it is shown and discussed that multilayer plasticity based on nested yield surfaces present some inconveniences when modelling multiaxial cyclic loading on the other hand the use of hardening surfaces instead of yield surfaces solves the problem partially it is also shown that multilayer plasticity based on the mroz kinematic rule yields clearly different multiaxial predictions when using the same uniaxial bilinear curve and different number of surfaces which is a priori inconsistent since the same monotonic stress strain curve should not result into a clearly different multiaxial behavior simply because of the discretization employed by the user it is demonstrated that in contrast with the mroz translation rule multilayer plasticity using the prager translation rule results in the same prediction regardless of the number of surfaces in which the hardening part of the bilinear curve is discretized this rule is also compliant with the principle of maximum dissipation it also allows for a vanishing elastic region without falling into theoretical or numerical difficulties hence it should not be discarded when developing advanced models

fixed rank kriging for very large spatial data sets summary spatial statistics for very large spatial data sets is challenging the size of the data set n causes problems in computing optimal spatial predictors such as kriging since its computa tional cost is of order a73 in addition a large data set is often defined on a large spatial domain so the spatial process of interest typically exhibits non stationary behaviour over that domain a flexible family of non stationary covariance functions is defined by using a set of basis functions that is fixed in number which leads to a spatial prediction method that we call fixed rank kriging specifically fixed rank kriging is kriging within this class of non stationary covariance functions it relies on computational simplifications when n is very large for obtaining the spatial best linear unbiased predictor and its mean squared prediction error for a hidden spatial process a method based on minimizing a weighted frobenius norm yields best estimators of the covari ance function parameters which are then substituted into the fixed rank kriging equations the new methodology is applied to a very large data set of total column ozone data observed over the entire globe where n is of the order of hundreds of thousands

random walks and random permutations a connection is made between the random turns model of vicious walkers and random permutations indexed by their increasing subsequences consequently the scaled distribution of the maximum displacements in a particular asymmeteric version of the model can be determined to be the same as the scaled distribution of the eigenvalues at the soft edge of the gue random hermitian matrices the scaling of the distribution gives the maximum mean displacement after t time steps as 2t 1 2 with standard deviation proportional to 1 3 the exponent 1 3 is typical of a large class of two dimensional growth problems

comments on the mroz multiple surface type plasticity models abstract several questions are addressed regarding the role of number of surfaces in the mroz type multiple surface models firstly increasing the number of surfaces improves the accuracy of the plastic modulus function but at the same time alters the translation behavior of surfaces two 90 out of phase axial torsion loading experiments are chosen to illustrate the number of surface influence on the model behavior the stresses exceed the experimental levels with increasing numbers of surfaces from 5 to 100 secondly for proportional loading the multiple surface models do not predict ratchetting progressive plastic strain accumulation in one direction however these models predict ratchetting for general nonproportional loading an ellipse shaped axial torsional loading path has been considered where predicted ratchetting rates far exceeded their experimental counter parts an explanation is forwarded to address these properties of the models it is further demonstrated that the multiple surface model of mroz and its modification by garud produce identical stress strain predictions when the number of surfaces exceeds a certain value for infinitesimal loading increment intersection of surfaces does not occur when using either the mroz or garud model however when finite loading increment is selected in numerical calculations the intersection problem arises in the mroz model

hybrid adaptive splines abstract an adaptive spline method for smoothing is proposed that combines features from both regression spline and smoothing spline approaches one of its advantages is the ability to vary the amount of smoothing in response to the inhomogeneous curvature of true functions at different locations this method can be applied to many multivariate function estimation problems which is illustrated by an application to smoothing temperature data on the globe the method s performance in a simulation study is found to be comparable to the wavelet shrinkage methods proposed by donoho and johnstone the problem of how to count the degrees of freedom for an adaptively chosen set of basis functions is addressed this issue arises also in the mars procedure proposed by friedman and other adaptive regression spline procedures

large deviations for wigner s law and voiculescu s non commutative entropy we study the spectral measure of gaussian wigner s matrices and prove that it satisfies a large deviation principle we show that the good rate function which governs this principle achieves its minimum value at wigner s semicircular law which entails the convergence of the spectral measure to the semicircular law as a conclusion we give some further examples of random matrices with spectral measure satisfying a large deviation principle and argue about voiculescu s non commutative entropy

efficient computation of smoothing splines via adaptive basis sampling summary smoothing splines provide flexible nonparametric regression estimators however the high computational cost of smoothing splines for large datasets has hindered their wide application in this article we develop a new method named adaptive basis sampling for efficient computation of smoothing splines in super large samples except for the univariate case where the reinsch algorithm is applicable a smoothing spline for a regression problem with sample size n can be expressed as a linear combination of n basis functions and its computational complexity is generally o n 3 we achieve a more scalable computation in the multivariate case by evaluating the smoothing spline using a smaller set of basis functions obtained by an adaptive sampling scheme that uses values of the response variable our asymptotic analysis shows that smoothing splines computed via adaptive basis sampling converge to the true function at the same rate as full basis smoothing splines using simulation studies and a large scale deep earth core mantle boundary imaging study we show that the proposed method outperforms a sampling method that does not use the values of response variables

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

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

uniform design theory and application a uniform design ud seeks design points that are uniformly scattered on the domain it has been popular since 1980 a survey of ud is given in the first portion the fundamental idea and construction method are presented and discussed and examples are given for illustration it is shown that ud s have many desirable properties for a wide variety of applications furthermore we use the global optimization algorithm threshold accepting to generate ud s with low discrepancy the relationship between uniformity and orthogonality is investigated it turns out that most ud s obtained here are indeed orthogonal

maximum projection designs for computer experiments summary space filling properties are important in designing computer experiments the traditional maximinandminimaxdistancedesignsconsideronlyspace fillinginthefull dimensionalspace thiscanresultinpoorprojectionsontolower dimensionalspaces whichisundesirablewhenonly af ew factors are active restricting maximin distance design to the class of latin hypercubes can improveone dimensionalprojectionsbutcannotguaranteegoodspace fillingpropertiesinlarger subspaces we propose designs that maximize space filling properties on projections to all subsets of factors we call our designs maximum projection designs our design criterion can be computed at no more cost than a design criterion that ignores projection properties

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

exact solution of the lock step model of vicious walkers the lock step model of vicious walkers on a one dimensional lattice allows each walker at the tick of a clock to move either one lattice site to the left or one lattice site to the right the only restriction is that no two walkers may arrive at the same lattice site or pass one another in periodic boundary conditions the partition function and correlation function for this model are calculated exactly taking the continuum limit gives an exactly solvable model of vicious walkers undergoing brownian motion

probability of survival for vicious walkers near a cliff the partition function for a model system of n vicious walkers is expressed as a determinant when the walkers are confined to a half line or a finite interval for the walkers on the half line the probability of survival the probability of a reunion and the conditional probability of a reunion are obtained the two point correlation near and parallel to a boundary of fixed like spins in the magnetised phase of the two dimensional ising model is conjectured to be proportional to the probability of a reunion near the boundary for n 2 and thus decay as e xi zeta r5 for large distances r

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

dominos and the gaussian free field we define a scaling limit of the height function on the domino tiling model dimer model on simply connected regions in z 2 and show that it is the massless free field a gaussian process with independent coefficients when expanded in the eigenbasis of the laplacian

statistical self similarity of one dimensional growth processes abstract for one dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times we argue that for self similar growth from a single seed the universal distribution is the tracy widom distribution from the theory of random matrices and that for the growth from a flat substrate it is some other only numerically determined distribution in particular for the polynuclear growth model in the droplet geometry the height maps onto the longest increasing subsequence of a random permutation from which the height distribution is identified as the tracy widom distribution

thin plate regression splines discuss the production of low rank smoothers for d greater than or equal to 1 dimensional data which can be fitted by regression or penalized regression methods the smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thin plate spline smoothing problem and are optimal in the sense that the truncation is designed to result in the minimum possible perturbation of the thin plate spline smoothing problem given the dimension of the basis used to construct the smoother by making use of lanczos iteration the basis change and truncation are computationally efficient the smoothers allow the use of approximate thin plate spline models with large data sets avoid the problems that are associated with knot placement that usually complicate modelling with regression splines or penalized regression splines provide a sensible way of modelling interaction terms in generalized additive models provide low rank approximations to generalized smoothing spline models appropriate for use with large data sets provide a means for incorporating smooth functions of more than one variable into non linear models and improve the computational efficiency of penalized likelihood models incorporating thin plate splines given that the approach produces spline like models with a sparse basis it also provides a natural way of incorporating unpenalized spline like terms in linear and generalized linear models and these can be treated just like any other model terms from the point of view of model selection inference and diagnostics

meissner phase for a model of oriented flux lines we consider a model of oriented non intersecting flux lines on the lattice zd where each flux line is assigned a boltzmann factor omega per unit length and a fugacity y we prove the existence of free energy both for y 0 and for y 1 and show that it is independent of y for y 0 using upper and lower bounds in terms of exactly solvable models we rigorously establish that for all y 0 the model has a phase transition at omega 1 d for omega 1 d we prove that the free energy and all bulk correlation functions vanish implying the exclusion of flux lines from the bulk in this regime we also show that the flux line density decays at least exponentially with distance from the boundary

implicit j2 bounding surface plasticity using prager s translation rule a bounding surface j2 plasticity model that uses prager s translation rule is presented the model preserves masing s rules and is developed from the same ideas as classical infinitesimal j2 plasticity resulting in the same formulation with the exception of the algorithm for the computation of the hardening function instead of utilizing a loading surface as in a previous formulation hardening surfaces are introduced the formulation is similar to that of multilayer plasticity using prager s rule presented in previous work an implicit algorithm based on the radial return concept is used and the consistent elastoplastic tangent is also developed in closed form examples illustrating anisotropic behaviour are presented and compared to that predicted by a multilayer j2 plasticity model the model is also applied to a soil dynamics problem to show the robustness of the algorithm and its applicability to complex loading copyright 2002 john wiley sons ltd

six vertex model with domain wall boundary conditions and one matrix model the partition function of the six vertex model on a square lattice with domain wall boundary conditions dwbc is rewritten as a hermitian one matrix model or a discretized version of it similar to sums over young diagrams depending on the phase the expression is exact for finite lattice size which is equal to the size of the corresponding matrix in the thermodynamic limit the matrix integral is computed using traditional matrix model techniques thus providing a complete treatment of the bulk free energy of the six vertex model with dwbc in the different phases in particular in the antiferroelectric phase the bulk free energy and a subdominant correction are given exactly in terms of elliptic theta functions

thermodynamic limit of the six vertex model with domain wall boundary conditions we address the question of the dependence of the bulk free energy on boundary conditions for the six vertex model here we compare the bulk free energy for periodic and domain wall boundary conditions using a determinant representation for the partition function with domain wall boundary conditions we derive toda differential equations and solve them asymptotically in order to extract the bulk free energy we find that it is different and bears no simple relation to the free energy for periodic boundary conditions the six vertex model with domain wall boundary conditions is closely related to algebraic combinatorics alternating sign matrices this implies new results for the weighted counting for large size alternating sign matrices finally we comment on the interpretation of our results in particular in connection with domino tilings dimers on a square lattice

strong asymptotics for krawtchouk polynomials we determine the strong asymptotics for the class of krawtchouk polynomials on the real line we show how our strong asymptotics describes the limiting distribution of the zeros of the krawtchouk polynomials

dimer pair correlations on the brick lattice using exact methods pair correlation functions are studied in the dimer model defined on a brick lattice at long distances these functions exhibit strongly anisotropic algebraic decay and near criticality the length scales diverge differently in the two principal directions the critical exponents are x 1 2 and y 1 these results are in agreement with deductions drawn from recent exact finite size scaling calculations we also interpret our results in the light of domain wall theories of commensurate incommensurate transitions and in particular we study the relation of the present model to the discrete version of the pokrovsky talapov model introduced by villain

sharp phase boundaries for a lattice flux line model we consider a model of nonintersecting flux lines in a rectangular region on the lattice mathbb z d where each flux line is a non isotropic self avoiding random walk constrained to begin and end on the boundary of the region the thermodynamic limit is reached through an increasing sequence of such regions we prove the existence of several distinct phases for this model corresponding to different regimes for the flux line density a phase with zero density a collection of phases with maximal density and at least one intermediate phase the locations of the boundaries of these phases are determined exactly for a wide range of parameters our results interpolate continuously between previous results on oriented and standard nonoriented self avoiding random walks

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