uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory we consider asymptotics for orthogonal polynomials with respect to varying exponential weights wn x dx e nv x dx on the line as n the potentials v are assumed to be real analytic with sufficient growth at infinity the principle results concern plancherel rotach type asymptotics for the orthogonal polynomials down to the axis using these asymptotics we then prove universality for a variety of statistical quantities arising in the theory of random matrix models some of which have been considered recently in 31 and also in 4 an additional application concerns the asymptotics of the recurrence coefficients and leading coefficients for the orthonormal polynomials see also 4 the orthogonal polynomial problem is formulated as a riemann hilbert problem following 19 20 the riemann hilbert problem is analyzed in turn using the steepest descent method introduced in 12 and further developed in 11 13 a critical role in our method is played by the equilibrium measure d v for v as analyzed in 8 1999 john wiley sons inc

vicious walks with a wall noncolliding meanders and chiral and bogoliubov de gennes random matrices spatially and temporally inhomogeneous evolution of one dimensional vicious walkers with wall restriction is studied we show that its continuum version is equivalent with a noncolliding system of stochastic processes called brownian meanders here the brownian meander is a temporally inhomogeneous process introduced by yor as a transform of the bessel process that is the motion of radial coordinate of the three dimensional brownian motion represented in spherical coordinates it is proved that the spatial distribution of vicious walkers with a wall at the origin can be described by the eigenvalue statistics of gaussian ensembles of bogoliubov de gennes hamiltonians of the mean field theory of superconductivity which have a particle hole symmetry we report that a time evolution of the present stochastic process is fully characterized by the change of symmetry classes from type c to type ci in the nonstandard classes of random matrix theory of altland and zirnbauer the relation between the noncolliding systems of the generalized meanders of yor which are associated with the even dimensional bessel processes and the chiral random matrix theory is also clarified

noncolliding brownian motion with drift and time dependent stieltjes wigert determinantal point process using the determinantal formula of biane bougerol and o connell we give multitime joint probability densities to the noncolliding brownian motion with drift where the number of particles is finite we study a special case such that the initial positions of particles are equidistant with a period a and the values of drift coefficients are well ordered with a scale we show that at each time t 0 the single time probability density of particle system is exactly transformed to the biorthogonal stieltjes wigert matrix model in the chern simons theory introduced by dolivet and tierz here one parameter extensions extensions of the stieltjes wigert polynomials which are themselves q extensions of the hermite polynomials play an essential role the two parameters a and of the process combined with time t are mapped to the parameters q and of the biorthogonal polynomials by the transformation of normalization factor of our probability density the partition function of the chern simons matrix model is readily obtained we study the determinantal structure of the matrix model and prove that at each time t 0 the present noncolliding brownian motion with drift is a determinantal point process in the sense that any correlation function is given by a determinant governed by a single integral kernel called the correlation kernel using the obtained correlation kernel we study time evolution of the noncolliding brownian motion with drift

solution of nester s gauge conditions we give a rigorous proof of the existence of solutions to the nonlinear gauge conditions on orthonormal frames introduced by nester to prove the positive energy theorem in general relativity the proof holds in all dimensions n 2 if the second de rham cohomology group vanishes one also proves uniqueness

a gauge condition for orthonormal three frames a set of natural gauge conditions for an orthonormal frame on a three dimensional riemannian manifold is discussed the conditions determine a teleparallel geometry they may be regarded as a nonlinear elliptic system for a rotation existence and uniqueness of solutions are discussed using the linearized system applications to einstein gravity are noted

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

fermionic construction of tau functions and random processes abstract tau functions expressed as fermionic expectation values e date m jimbo m kashiwara t miwa transformation groups for soliton equations in m jimbo t miwa eds nonlinear integrable systems classical theory and quantum theory world scientific 1983 pp 39 120 are shown to provide a natural and straightforward description of a number of random processes and statistical models involving hard core configurations of identical particles on the integer lattice like a discrete version simple exclusion processes asep nonintersecting random walkers lattice coulomb gas models and others as well as providing a powerful tool for combinatorial calculations involving paths between pairs of partitions we study the decay of the initial step function within the discrete asep d asep model as an example for constant hopping rates we obtain vershik kerov type of asymptotic configuration of particles

strong asymptotics of orthogonal polynomials with respect to exponential weights we consider asymptotics of orthogonal polynomials with respect to weights w x dx e q x dx on the real line where q x 2m k 0 qkx k q2m 0 denotes a polynomial of even order with positive leading coefficient the orthogonal polynomial problem is formulated as a riemann hilbert problem following 22 23 we employ the steepest descent type method introduced in 18 and further developed in 17 19 in order to obtain uniform plancherel rotach type asymptotics in the entire complex plane as well as asymptotic formulae for the zeros the leading coefficients and the recurrence coefficients of the orthogonal polynomials c 1999 john wiley sons inc

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

the asymptotics of monotone subsequences of involutions we compute the limiting distributions of the lengths of the longest monotone subsequences of random signed involutions with or without conditions on the number of fixed points and negated points as the sizes of the involutions tend to infinity the resulting distributions are depending on the number of fixed points 1 the tracy widom distributions for the largest eigenvalues of random goe gue gse matrices 2 the normal distribution or 3 new classes of distributions which interpolate between pairs of the tracy widom distributions we also consider the second rows of the corresponding young diagrams in each case the convergence of moments is also shown the proof is based on the algebraic work of j baik and e rains in 7 which establishes a connection between the statistics of random involutions and a family of orthogonal polynomials and an asymptotic analysis of the orthogonal polynomials which is obtained by extending the riemann hilbert analysis for the orthogonal polynomials by p deift k johansson and baik in 3

discrete painleve equations and their appearance in quantum gravity we discuss an algorithmic approach for both deriving discrete analogues of painleve equations as well as using such equations to characterize similarity reductions of spatially discrete integrable evolution equations as a concrete example we show that a discrete analogue of painleve i can be used to characterize similarity solutions of the kac moerbeke equation it turns out that these similarity solutions also satisfy a special case of painleve iv equation in addition we discuss a methodology for obtaining the relevant continuous limits not only at the level of equations but also at the level of solutions as an example we use the wkb method in the presence of two turning points of the third order to parametrize at the continuous limit the solution of painleve i in terms of the solution of discrete painleve i finally we show that these results are useful for investigating the partition function of the matrix model in 2d quantum gravity associated with the measure exp t1z2 t2z4 t3z6

high effective finite element algorithm for elliptic partial differential equation in this paper we will discuss elliptic partial differential equation whose coefficients are constants on basis of a new computing technique for green function we will propose a new effective finite element algorithm for that problem finally we will give some numerical examples to investigate that finite element algorithm

on random matrices from the compact classical groups if m is a matrix taken randomly with respect to normalized haar measure on u n o n or sp n then the real and imaginary parts of the random variables tr mk k 1 converge to independent normal random variables with mean zero and variance k 2 as the size n of the matrix goes to infinity for the unitary group this is a direct consequence of the strong szeg6 theorem for toeplitz determinants we will prove a conjecture of diaconis

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

the post processing approach in the finite element method part 1 calculation of displacements stresses and other higher derivatives of the displacements this is the first in a series of three papers in which we discuss a method for post processing a finite element solution to obtain high accuracy approximations for displacements stresses stress intensity factors etc rather than take the values of these quantities directly from the finite element solution we evaluate certain weighted averages of the solution over the entire region these yield approximations are of the same order of accuracy as the strain energy we obtain error estimates and also present some numerical examples to illustrate the practical effectiveness of the technique in the third paper of this series we address the matters of adaptive mesh selection and a posteriori error estimation

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

a filter method for solving nonlinear complementarity problems filter methods are extensively studied to handle nonlinear programming problems recently because of good numerical results filter techniques are attached importance to in this paper filter approaches are employed to tackle nonlinear complementarity problems ncps firstly ncp conditions are transformed into a nonlinear programming problem then to obtain a trial step the corresponding nonlinear programming problems are solved by some existing strategies moreover filter criterion is utilized to evaluate a trial iterate the purpose in this paper is to employ filter approaches to attack ncps in essence multi objective view is utilized to attack ncps because the idea of filter methods stems from multi objective problems furthermore a new filter method based on the special two objects which differs from others is brought forward moreover maratos effects are overcome in our new filter approach by weakening acceptable conditions

interior maximum norm estimates for finite element methods part ii we consider bilinear forms a connected with second order elliptic problems and assume that for u h in a finite element space s h we have a u u h x f x for x in s h with local compact support we give local estimates for u u h in l and w 1 of the type local best approximation plus weak outside influences plus the local size of f

knot points of a double covariant system of elliptic equations and preferred frames in general relativity we investigate the elliptic system of equations which is general covariant and locally su 2 covariant for this system we obtain the new condition of the dirichlet problem solvability and the condition of the absence of zeroes for the solutions this system contains in particular the sen witten equation on this basis we prove the existence of the wide class of hypersurfaces in all points of which there exists a correspondence between the sen witten spinor field and three frames as well as preferred lapses and shifts the nester special orthonormal frame also exists on a certain subclass containing not just the maximal hypersurfaces

moments of vicious walkers and mobius graph expansions a system of brownian motions in one dimension all started from the origin and conditioned never to collide with each other in a given finite time interval 0 t is studied the spatial distribution of such vicious walkers can be described by using the repulsive eigenvalue statistics of random hermitian matrices and it was shown that the present vicious walker model exhibits a transition from the gaussian unitary ensemble gue statistics to the gaussian orthogonal ensemble goe statistics as the time t goes on from 0 to t in the present paper we characterize this gue to goe transition by presenting the graphical expansion formula for the moments of positions of vicious walkers in the gue limit stackrel ensuremath rightarrow t 0 only the ribbon graphs contribute and the problem is reduced to the classification of orientable surfaces by genus following the time evolution of the vicious walkers however the graphs with twisted ribbons called m obius graphs increase their contribution to our expansion formula and we have to deal with the topology of nonorientable surfaces application of the recent exact result of dynamical correlation functions yields closed expressions for the coefficients in the m obius expansion using the stirling numbers of the first kind

the reunions of three dissimilar vicious walkers we study the behavior of three vicious random walkers which diffuse freely in one dimension witharbitrary diffusivitiesb 1 2 b 2 2 b 3 2 except that their paths may not cross the full distribution function is calculated exactly in the continuum limit the exponent 3 governing the decay of the probability r n 3 sim 1 n psi 3 of a simultaneousreunion of all three walkers aftern steps is found to varycontinuously according to psi 3 1 pi cos 1 left b 2 2 left b 1 2 b 2 2 b 2 2 b 3 2 right 1 2 right this variation has consequences for various interfacial wetting transitions in 1 1 dimensions it may also be related heuristically to the marginality of direct interface wall interactions decaying asw0 l2 in the intermediate fluctuation regime of 1 1 dimensional wetting where exponents varying continuously withw0 have recently been found

capture time of brownian pursuits let b 0 b 1 b n be independent standard brownian motions starting at 0 we investigate the tail of the capture time where 0 b i 1 1 i n in particular we have 3 and 5 various generalizations are also studied

vicious walkers and young tableaux i without walls we rederive previously known results for the number of star and watermelon configurations by showing that these follow immediately from standard results in the theory of young tableaux and integer partitions in this way we provide a proof of a result previously only conjectured for the total number of stars

fluctuations of the one dimensional polynuclear growth model in half space we consider the multi point equal time height fluctuations of the one dimensional polynuclear growth model in half space for special values of the nucleation rate at the origin the multi layer version of the model is reduced to a process with a determinantal weight for which the asymptotics can be analyzed in the scaling limit the fluctuations near the origin are shown to be equivalent to those of the largest eigenvalue of the orthogonal symplectic to unitary transition ensemble at soft edge in random matrix theory

algebraic aspects of increasing subsequences we present a number of results relating partial cauchy littlewood sums integrals over the compact classical groups and increasing subsequences of permutations these include integral formulae for the distribution of the longest increasing subsequence of a random involution with constrained number of fixed points new formulae for partial cauchy littlewood sums as well as new proofs of old formulae relations of these expressions to orthogonal polynomials on the unit circle and explicit bases for invariant spaces of the classical groups together with appropriate generalizations of the straightening algorithm

a normal comparison inequality and its applications let xi xi i 1 leq i leq n and eta eta i 1 leq i leq n be standard normal random variables with covariance matrices r 1 r ij 1 and r 0 r ij 0 respectively slepian s lemma says that if r ij 1 geq r ij 0 for 1 leq i j leq n the lower bound p xi i leq u mb for 1 leq i leq n p eta i leq u mb for 1 leq i leq n is at least 1 in this paper an upper bound is given the usefulness of the upper bound is justified with three concrete applications i the new law of the iterated logarithm of erd s and revesz ii the probability that a random polynomial does not have a real zero and iii the random pursuit problem for fractional brownian particles in particular a conjecture of kesten 1992 on the random pursuit problem for brownian particles is confirmed which leads to estimates of principal eigenvalues

a combinatorial interpretation of the free fermion condition of the six vertex model the free fermion condition of the six vertex model provides a five parameter sub manifold on which the bethe ansatz equations for the wavenumbers that enter into the eigenfunctions of the transfer matrices of the model decouple hence allowing explicit solutions such conditions arose originally in early field theoretic s matrix approaches here we provide a combinatorial explanation for the condition in terms of a generalized gessel viennot involution by doing so we extend the use of the gessel viennot theorem originally devised for non intersecting walks only to a special weighted type of intersecting walk and hence express the partition function of n such walks starting and finishing at fixed endpoints in terms of the single walk partition functions

a new superconvergence and extrapolation for second order triangular element in this paper we find a new superconvergence and extrapolation for second order triangular element based on w m he j z cui q d zhu an improved method on superconvergence and extrapolation math numer sinica 24 2002 3 in chinese of course some numerical examples are given to investigate those estimates

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

asymptotic error expansion and richardson extrapolation for linear fine elements the elliptic ritz projection with linear finite elements is shown to admit asymptotic error expansions on certain uniform meshes this justifies the application of richardson extrapolation for increasing the accuracy

critical behavior of nonintersecting brownian motions at a tacnode we study a model of n one dimensional nonintersecting brownian motions with two prescribed starting points at time t 0 and two prescribed ending points at time t 1 in a critical regime where the paths fill two tangent ellipses in the time space plane as n the limiting mean density for the positions of the brownian paths at the time of tangency consists of two touching semicircles possibly of different sizes we show that in an appropriate double scaling limit there is a new family of limiting determinantal point processes with integrable correlation kernels that are expressed in terms of a new riemann hilbert problem of size 4 4 we prove solvability of the riemann hilbert problem and establish a remarkable connection with the hastings mcleod solution of the painleve ii equation we show that this painleve ii transcendent also appears in the critical limits of the recurrence coefficients of the multiple hermite polynomials that are associated with the nonintersecting brownian motions universality suggests that the new limiting kernels apply to more general situations whenever a limiting mean density vanishes according to two touching square roots which represents a new universality class 2011 wiley periodicals inc

ordering of random walks the leader and the laggard we investigate two complementary problems related to maintaining the relative positions of n random walks on the line i the leader problem that is the probability n t that the leftmost particle remains the leftmost as a function of time and ii the laggard problem the probability n t that the rightmost particle never becomes the leftmost we map these ordering problems onto an equivalent n 1 dimensional electrostatic problem from this construction we obtain a very accurate estimate for n t for n 4 the first case that is not exactly solvable 4 t t 4 with 4 0 91342 8 the probability of being the laggard also decays algebraically n t t n we derive 2 1 2 3 3 8 and argue that n n 1 ln n as n

vicious walkers friendly walkers and young tableaux ii with a wall we derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory of young tableaux and combinatorial descriptions of symmetric functions for the problem of n friendly walkers we derive exact asymptotics for the number of stars and watermelons both in the absence of a wall and in the presence of a wall

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

exact solution of n directed non intersecting walks interacting with one or two boundaries the partition function for the problem of an arbitrary number of directed non intersecting walks interacting with one or two walls parallel to the direction of the walks is calculated exactly utilizing a theorem recently proved concerning the bethe ansatz for the eigenvectors of the transfer matrix of the five vertex model this theorem shows that the completeness of the bethe ansatz eigenvectors for the n walk transfer matrix can be deduced from the completeness of the one walk eigenvectors

large n limit of gaussian random matrices with external source part i we continue the study of the hermitian random matrix ensemble with external source open image in new window where a has two distinct eigenvalues a of equal multiplicity this model exhibits a phase transition for the value a 1 since the eigenvalues of m accumulate on two intervals for a 1 and on one interval for 0 1 was treated in part i where it was proved that local eigenvalue correlations have the universal limiting behavior which is known for unitarily invariant random matrices that is limiting eigenvalue correlations are expressed in terms of the sine kernel in the bulk of the spectrum and in terms of the airy kernel at the edge in this paper we establish the same results for the case 0 a 1 as in part i we apply the deift zhou steepest descent analysis to a 3 3 matrix riemann hilbert problem due to the different structure of an underlying riemann surface the analysis includes an additional step involving a global opening of lenses which is a new phenomenon in the steepest descent analysis of riemann hilbert problems

the post processing approach in the finite element method part 2 the calculation of stress intensity factors abstract in the context of a model problem the authors describe post processing techniques for the calculation of generalized stress intensity factors they discuss two broad classes of methods one involving an influence function and the other related to the well known energy release principle of fracture mechanics an error analysis is sketched and two numerical examples are given to illustrate the effectivity of the techniques this is the second in a series of three papers author

families of vicious walkers we consider a generalization of the vicious walker problem in which n random walkers in rd are grouped into p families using field theoretic renormalization group methods we calculate the asymptotic behaviour of the probability that no pairs of walkers from different families have met up to time t for d 2 this is constant but for d 2 it decays as a power t which we compute to e2 in an expansion in e 2 d the second order term depends on the ratios of the diffusivities of the different families in two dimensions we find a logarithmic decay ln t and compute exactly

special orthonormal frames a natural gauge condition is used to select special orthonormal frames and thereby a preferred teleparallel geometry on a riemannian manifold of any dimension the condition is equivalent to a nonlinear elliptic system for a rotation existence and uniqueness of solutions are discussed certain special cases and applications are noted

extrapolation techniques for reducing the pollution effect or reentrant corners in the finite element method standard finite element schemes applied to boundary value problems on domains with reentrant corners suffer from a global loss of accuracy caused by the influence of the corner singularities for a model situation it is shown that this pollution effect can be completely described in terms of an asymptotic error expansion with respect to fractional powers of the mesh size parameter this provides the basis of an extrapolation procedure which recovers the full order of accuracy for the solution as well as for the corresponding stress intensity factors

vicious walkers friendly walkers and young tableaux iii between two walls we derive exact and asymptotic results for the number of star and watermelon configurations of vicious walkers confined to lie between two impenetrable walls as well as corresponding results for the analogous problem of friendly walkers our proofs make use of results from symmetric function theory and the theory of basic hypergeometric series

nonintersecting brownian bridges on the unit circle with drift abstract nonintersecting brownian bridges on the unit circle form a determinantal stochastic process exhibiting random matrix statistics for large numbers of walkers we investigate the effect of adding a drift term to walkers on the circle conditioned to start and end at the same position for each return time t 2 we show there exists a critical drift c t such that if 2 m t c t for some integer m then the expected winding number for each walker is asymptotically m in addition we compute the asymptotic distribution of total winding numbers in the double scaling regime in which the expected number of walkers with winding number not equal to m is finite the method of proof is riemann hilbert analysis of a certain family of discrete orthogonal polynomials with varying complex exponential weights this is the first asymptotic analysis of such a class of polynomials we determine asymptotic formulas for these polynomials as the degree of the polynomial grows large and demonstrate the emergence of a second band of zeros by a mechanism not previously seen for discrete orthogonal polynomials with real weights

scaling limit of vicious walks and two matrix model we consider the diffusion scaling limit of the one dimensional vicious walker model of fisher and derive a system of nonintersecting brownian motions the spatial distribution of n particles is studied and it is described by use of the probability density function of eigenvalues of nxn gaussian random matrices the particle distribution depends on the ratio of the observation time t and the time interval t in which the nonintersecting condition is imposed as t t is going on from 0 to 1 there occurs a transition of distribution which is identified with the transition observed in the two matrix model of pandey and mehta despite of the absence of matrix structure in the original vicious walker model in the diffusion scaling limit accumulation of contact repulsive interactions realizes the correlated distribution of eigenvalues in the multimatrix model as the particle distribution

random matrix central limit theorems for nonintersecting random walks we consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function we prove that in a certain limiting regime where the number of walks and the number of time steps grow to infinity several limiting distributions of the walks at the mid time behave as the eigenvalues of random hermitian matrices as the dimension of the matrices grows to infinity

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