conditional intensity and gibbsianness of determinantal point processes the papangelou intensities of determinantal or fermion point processes are investigated these exhibit a monotonicity property expressing the repulsive nature of the interaction and satisfy a bound implying stochastic domination by a poisson point process we also show that determinantal point processes satisfy the so called condition which is a general form of gibbsianness under a continuity assumption the gibbsian conditional probabilities can be identified explicitly

a numerical method for an integro differential equation with memory in banach spaces qualitative properties a first order method is considered for the discretization in time of an integro differential equation which can be written as d alpha u t a u t f t 1 alpha 2 where a d a subset x to x is a sectorial operator in a banach space x qualitative properties of the numerical solution such as contractivity and positivity are studied a numerical illustration is provided

a connection formula for the second painleve transcendent we consider a particular case of the second painleve transcendent y xy 2y 3 it is known that if y x kai x as x then if 0 k 1 y x sim d left x right raise0 5ex hbox scriptstyle 1 kern 0 1em kern 0 15em lower0 25ex hbox scriptstyle 4 sin frac 2 3 left x right 3 2 frac 3 4 d2 ell n left x right c asx to infty where d k and c k are the connection formulae for this nonlinear ordinary differential equation

analytical depoissonization and its applications in combinatorics and analysis of algorithms a poisson version of a problem henceforth called a poisson model or poissonization is often easier to solve than the original one which we name here the bernoulli model poissonization is a technique that replaces the original input e g think of balls thrown into urns by a poisson process e g think of balls arriving according to a poisson process into urns more precisely analytical poisson transform maps a sequence e g characterizing the bernoulli model into a generating function of a complex variable however after poissonization one must depoissonize in order to translate the results of the poisson model into the original i e bernoulli model we present in this paper several analytical depoissonization results that fall into the following general scheme if the poisson transform has an appropriate growth in the complex plane then an asymptotic expansion of the sequence can be expressed in terms of the poisson transform and its derivatives evaluated on the real line not surprisingly actual formulations of depoissonization results depend on the nature of the growth of the poisson transform and thus we have polynomial and exponential depoissonization theorems normalization e g as in the central limit theorem introduces another twist that led us to formulate the so called diagonal depoissonization theorems finally we illustrate our results on numerous examples from combinatorics and the analysis of algorithms and data structures e g combinatorial assemblies digital trees multiaccess protocols probabilistic counting selecting a leader data compression etc authors abstract

an asymptotically least favorable chernoff bound for a large class of dependent data processes it is desired to determine the worst case asymptotic error probability performance of a given detector operating in an environment of uncertain data dependency a class of markov data process distributions is considered which satisfy a one shift dependency bound and agree with a specified univariate distribution within this dependency contamination class the distribution structure which minimizes the exponential rate of decrease of detection error probabilities is identified this is a uniform least favorability principle because the least favorable dependency structure is the same for all bounded memoryless detectors the error probability exponential rate criterion used is a device of large deviations theory the results agree well with previous results obtained using pitman s asymptotic relative efficiency are which is a more tractable small signal performance criterion in contrast to are large deviations theory is closely related to finite sample error probabilities via the finite sample chernoff bounds and other exponentially tight bounds and other approximations

weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations this paper is concerned with the existence and uniqueness of a weighted pseudo almost automorphic mild solution to the semilinear fractional equation d t au t au t d t a 1f t u t t r 1 a 2 in complex banach spaces with s p weighted pseudo almost automorphic coefficients where a is a linear densely defined operator of sectorial type on a complex banach space x moreover we present an application to a fractional wave equation

existence of s asymptotically ω periodic solutions to abstract integro differential equations we study the existence of solutions for a class of abstract equations we construct an exponentially stable resolvent operator solutions s asymptotically periodic are obtained we obtained existence results with less restrictions on the constants we provide a concrete example for the abstract results the main aim of this work is to study the existence of s asymptotically periodic solutions for a class of abstract integro differential equations modeled in the following form d dt x t 0 t n t s x s ds ax t 0 t b t s x s ds f t x t t 0 x 0 x 0 x where a b t for t 0 are closed linear operators defined on a common domain d a which is dense in x n t for t 0 are bounded linear operators on x and f 0 i x x is an appropriate function the existence results are obtained by applying the theory of exponentially stable resolvent operators we also discuss an application of these results

averages of characteristic polynomials in random matrix theory we compute averages of products and ratios of characteristic polynomials associated with orthogonal unitary and symplectic ensembles of random matrix theory the pfaffian determinantal formulae for these averages are obtained and the bulk scaling asymptotic limits are found for ensembles with gaussian weights classical results for the correlation functions of the random matrix ensembles and their bulk scaling limits are deduced from these formulae by a simple computation we employ a discrete approximation method the problem is solved for discrete analogues of random matrix ensembles originating from representation theory and then a limit transition is performed exact pfaffian determinantal formulae for the discrete averages are proven using standard tools of linear algebra no application of orthogonal or skew orthogonal polynomials is needed 2005 wiley periodicals inc

large deviation probabilities and dominating points for open convex sets nonlogarithmic behavior the existence of a dominating point for an open convex set and a corresponding representation formula for large deviation probabilities are established in the infinite dimensional setting under conditions which are both necessary and sufficient and follow from those used previously in mathbb r d a precise nonlogarithmic estimate of large deviation probabilities applicable to gaussian measures is also included

s asymptotically ω periodic and asymptotically ω periodic solutions to semi linear cauchy problems with non dense domain abstract in this work we study the existence and uniqueness of s asymptotically periodic and asymptotically periodic solutions to a first order differential equation with linear part dominated by a hille yosida operator with non dense domain applications to partial differential equations fractional integro differential and neutral differential equations are given

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

integrals over grassmannians and random permutations testing the independence of two gaussian populations involves the distribution of the sample canonical correlation coefficients given that the actual correlation is zero the laplace transform as a function of x of this distribution is not only an integral over the grassmannian gr p f n of p dimensional planes in real complex or quaternion n space f n but is also related to a generalized hypergeometric function such integrals are solutions of painleve like equations in the complex case they are solutions to genuine painleve equations these integrals over gr p c n have remarkable expansions in x related to random words of length l formed with an alphabet of p letters 1 p the coefficients of these expansions are given by the probability that a word i contains a subsequence of letters p p 1 1 in that order and ii that the maximal length of the disjoint union of p 1 increasing subsequences of the word is less than or equal tok where k refers to the power of x note that if each letter appears in the word then the maximal length of the disjoint union of p increasing subsequences of the word is automatically l and is thus trivial c 2003 elsevier inc all rights reserved

regularized solutions for abstract volterra equations abstract we introduce a two kernel dependent family of strong continuous operators defined in a banach space which allows us to consider in an unified treatment the notions of among others c 0 semigroups of operators cosine families n times integrated semigroups resolvent families and k generalized solutions the results are applied to the study of existence and uniqueness of solutions for the volterra equation of convolution type u f a au in the case a is not necessarily densely defined examples for equations defined in l p spaces are also given

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

topological recursion in enumerative geometry and random matrices we review the method of symplectic invariants recently introduced to solve matrix models loop equations in the so called topological expansion and further extended beyond the context of matrix models for any given spectral curve one defines a sequence of differential forms and a sequence of complex numbers fg called symplectic invariants we recall the definition of fg s and we explain their main properties in particular symplectic invariance integrability modularity as well as their limits and their deformations then we give several examples of applications in particular matrix models enumeration of discrete surfaces maps algebraic geometry and topological strings and non intersecting brownian motions

asymptotically periodic solutions of abstract differential equations abstract in this paper we introduce the concept of s asymptotically periodicity in the stepanov sense we study some properties of the space consisting of s asymptotically periodic functions and we use this notion to establish the existence of s asymptotically periodic solutions to linear and semi linear first order abstract differential equations in particular we characterize the strongly continuous semigroups of bounded linear operators defined on reflexive spaces which are s asymptotically periodic as those semigroups which are the direct sum of an periodic and a strongly stable semigroup

stein s method and plancherel measure of the symmetric group we initiate a stein s method approach to the study of the plancherel measure of the symmetric group a new proof of kerov s central limit theorem for character ratios of random representations of the symmetric group on transpositions is obtained the proof gives an error term the construction of an exchangeable pair needed for applying stein s method arises from the theory of harmonic functions on bratelli diagrams we also find the spectrum of the markov chain on partitions underlying the construction of the exchangeable pair this yields an intriguing method for studying the asymptotic decomposition of tensor powers of some representations of the symmetric group

weighted pseudo almost periodic functions and applications to evolution equations with delay in this paper we introduce a new class of vector valued weighted pseudo almost periodic functions and present some basic properties about these new functions moreover we obtain an new existence theorem of vector valued weighted pseudo almost periodic solution to the evolution equations x t ax t f t x t with delay in a banach space x

the asep and determinantal point processes we introduce a family of discrete determinantal point processes related to orthogonal polynomials on the real line with correlation kernels defined via spectral projections for the associated jacobi matrices for classical weights we show how such ensembles arise as limits of various hypergeometric orthogonal polynomial ensembles we then prove that the q laplace transform of the height function of the asep with step initial condition is equal to the expectation of a simple multiplicative functional on a discrete laguerre ensemble a member of the new family this allows us to obtain the large time asymptotics of the asep in three limit regimes a for finitely many rightmost particles b gue tracy widom asymptotics of the height function c kpz asymptotics of the height function for the asep with weak asymmetry we also give similar results for two instances of the stochastic six vertex model in a quadrant the proofs are based on limit transitions for the corresponding determinantal point processes

asymptotics of q plancherel measures in this paper we are interested in the asymptotic size of the rows and columns of a random young diagram under a natural deformation of the plancherel measure coming from hecke algebras the first lines of such diagrams are typically of order n so it does not fit in the context of the work of biane int math res notices 4 179 192 2001 and niady probab theory relat fields 136 263 297 2006 using the theory of polynomial functions on young diagrams of kerov and olshanski we are able to compute explicitly the first and second order asymptotics of the length of the first rows our method also works for other measures for example those coming from schur weyl representations

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

gaussian fluctuation for the number of particles in airy bessel sine and other determinantal random point fields we prove the central limit theorem clt for the number of eigenvalues near the spectrum edge for certain hermitian ensembles of random matrices to derive our results we use a general theorem essentially due to costin and lebowitz concerning the gaussian fluctuation of the number of particles in random point fields with determinantal correlation functions as another corollary of the costin lebowitz theorem we prove the clt for the empirical distribution function of the eigenvalues of random matrices from classical compact groups

weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations abstract this paper is concerned with the existence and uniqueness of weighted pseudo almost automorphic mild solution to the semilinear fractional equation d t u t au t d t 1 f t u t bu t t r 1 2 where a is a linear densely defined operator of sectorial type on a complex banach space x and b is a bounded linear operator defined on x under the assumption of uniformly continuity on f we establish a composition of weighted pseudo almost automorphic in a general banach space and obtain existence results by means of banach contraction mapping the results obtained are utilized to study the existence and uniqueness of a weighted pseudo almost automorphic solution to fractional diffusion wave equation with dirichlet conditions

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

cauchy problem for fractional diffusion equations abstract we consider an evolution equation with the regularized fractional derivative of an order 0 1 with respect to the time variable and a uniformly elliptic operator with variable coefficients acting in the spatial variables such equations describe diffusion on inhomogeneous fractals a fundamental solution of the cauchy problem is constructed and investigated

nonexistence of periodic solutions and s asymptotically periodic solutions in fractional difference equations nonexistence of periodic solution is proved for periodic right hand side existence of s asymptotically periodic solutions is discussed existence and uniqueness results are obtained for s asymptotically periodic solution nontrivial estimations of a ratio of gamma functions are used in this paper it is shown that a fractional difference equation with a periodic right hand side can not possess a periodic solution but it can have an s asymptotically periodic solution sufficient conditions are proved for the existence of a unique s asymptotically periodic solution an example is also given illustrating the obtained results

longest increasing subsequences from patience sorting to the baik deift johansson theorem we describe a simple one person card game patience sorting its analysis leads to a broad circle of ideas linking young tableaux with the longest increasing subsequence of a random permutation via the schensted correspondence a recent highlight of this area is the work of baik deift johansson which yields limiting probability laws via hard analysis of toeplitz determinants

eynard mehta theorem schur process and their pfaffian analogs we give simple linear algebraic proofs of the eynard mehta theorem the okounkov reshetikhin formula for the correlation kernel of the schur process and pfaffian analogs of these results we also discuss certain general properties of the spaces of all determinantal and pfaffian processes on a given finite set

on s asymptotically ω periodic functions and applications abstract let x be a banach space and r a bounded function u c 0 x is called s asymptotically periodic if lim t u t u t 0 in this paper we establish conditions under which an s asymptotically periodic function is asymptotically periodic and we discuss the existence of s asymptotically periodic and asymptotically periodic solutions for an abstract integral equation some applications to partial differential equations and partial integro differential equations are considered

existence of s asymptotically ω periodic solutions for fractional order functional integro differential equations with infinite delay abstract we study s asymptotically periodic solutions of the abstract fractional equation u 1 a u f t u t 1 2 where a is a linear operator of sectorial type 0

s asymptotically ω positive periodic solutions for a class of neutral fractional differential equations in this paper we investigate the existence of the s asymptotically positive periodic solutions to a class of semilinear neutral caputo fractional differential equations with infinite delay given by d t x t f t x t a x t g t x t t 0 x 0 b the function is considered in a banach space x for 0 1 here a denotes the infinitesimal generator of an analytic semigroup t t t 0

dominating points and large deviations for random vectors we establish a representation formula useful for obtaining precise large deviation probabilities for convex open subsets of a banach space these estimates are based on the existence of dominating points in this setting

on a class of retarded integro differential equations with nonlocal initial conditions of concern is the following cauchy problem for fractional integro differential equations with time delay and nonlocal initial condition u t email protected 0 t t s m email protected m 1 au s ds f t u t u k t t 0 u t h t u email protected t email protected email protected 0 where 1 0 a d a x x is a generator of a solution operator on a complex banach space x the convolution integral in the equation is known as the riemann liouville fractional integral k t 0 email protected representing the delay property is a function and h t is an operator defined from email protected 0 xc email protected 0 x into x for some t 0 which constitutes a nonlocal condition the local existence and uniqueness of mild solutions for the cauchy problem under various criteria are proved moreover we present an existence result of the global solution also an example is given to illustrate the applications of the abstract results

a probabilistic interpretation of the macdonald polynomials the two parameter macdonald polynomials are a central object of algebraic combinatorics and representation theory we give a markov chain on partitions of k with eigenfunctions the coefficients of the macdonald polynomials when expanded in the power sum polynomials the markov chain has stationary distribution a new two parameter family of measures on partitions the inverse of the macdonald weight rescaled the uniform distribution on cycles of permutations and the ewens sampling formula are special cases the markov chain is a version of the auxiliary variables algorithm of statistical physics properties of the macdonald polynomials allow a sharp analysis of the running time in natural cases a bounded number of steps suffice for arbitrarily large k

on linear systems and τ functions associated with lame s equation and painleve s equation vi abstract painleve s transcendental differential equation p vi may be expressed as the consistency condition for a pair of linear differential equations with 2 2 matrix coefficients with rational entries by a construction due to tracy and widom this linear system is associated with certain kernels which give trace class operators on hilbert space this paper expresses such operators in terms of hankel operators of linear systems which are realised in terms of the laurent coefficients of the solutions of the differential equations let p t l 2 0 l 2 t be the orthogonal projection then the fredholm determinant t det i p t defines the function which is here expressed in terms of the solution of a matrix gelfand levitan equation for suitable values of the parameters solutions of the hypergeometric equation give a linear system with similar properties for meromorphic transfer functions that have poles on an arithmetic progression the corresponding hankel operator has a simple form with respect to an exponential basis in l 2 0 so det i p t can be expressed as a series of finite determinants this applies to elliptic functions of the second kind such as satisfy lame s equation with l 1

fredholm determinants jimbo miwa ueno τ functions and representation theory the authors show that a wide class of fredholm determinants arising in the representation theory of big groups such as the infinite dimensional unitary group solve painleve equations their methods are based on the theory of integrable operators and the theory of riemann hilbert problems 2002 wiley periodicals inc

regularity of mild solutions for a class of fractional order differential equations in this article we show sufficient conditions ensuring the existence and uniqueness of a mild solution to the equation d au t au t d a 1f t u t 1 a 2 email protected r in the same space where f belongs here a is a sectorial operator defined in a banach space x d a is the fractional derivative in the riemann liouville sense and f x email protected x for each email protected x where w x is a vector valued subspace of the space of continuous and bounded functions the subspaces w x that we will consider in this article are the space of periodic almost periodic almost automorphic and compact almost automorphic vector valued functions among others in particular we extend and unify recent results established for the equation in the papers agarwal et al 2010 cuevas et al 2010 and cuevas and lizama 2008

random words toeplitz determinants and integrable systems ii this paper connects the analysis of the length of the longest weakly increasing subsequence of inhomogeneous random words to a riemnn hilbert problem and an associated system of integrable partial differential equations in particular we show that the poissonization of the distribution function of this length can be identified as the jimbo miwa ueno tau function

duality of orthogonal polynomials on a finite set we prove a certain duality relation for orthogonal polynomials defined on a finite set the result is used in a direct proof of the equivalence of two different ways using particles or holes of computing the correlation functions of a discrete orthogonal polynomial ensemble

on s asymptotically ω periodic functions on banach spaces and applications abstract this paper is devoted to the study of the class of continuous and bounded functions f 0 x for which exists 0 such that lim t f t f t 0 in the sequel called s asymptotically periodic functions we discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically periodic functions we also study the existence of s asymptotically periodic mild solutions of the first order abstract cauchy problem in banach spaces

pseudo s asymptotically periodic solutions of second order abstract cauchy problems in this work we discuss the existence of pseudo s asymptotically periodic mild solutions for a second order abstract cauchy problem in particular we show that pseudo s asymptotically periodic cosine functions of operators are periodic the paper is completed with an application to the nonautonomous wave equation

random sorting networks local statistics via random matrix laws this paper finds the bulk local limit of the swap process of uniformly random sorting networks the limit object is defined through a deterministic procedure a local version of the edelman greene algorithm applied to a two dimensional determinantal point process with explicit kernel the latter describes the asymptotic joint law near 0 of the eigenvalues of the corners in the antisymmetric gaussian unitary ensemble in particular the limiting law of the first time a given swap appears in a random sorting network is identified with the limiting distribution of the closest to 0 eigenvalue in the antisymmetric gue moreover the asymptotic gap in the bulk between appearances of a given swap is the gaudin mehta law the limiting universal distribution for gaps between eigenvalues of real symmetric random matrices the proofs rely on the determinantal structure and a double contour integral representation for the kernel of random poissonized young tableaux of arbitrary shape

painleve formulas of the limiting distributions for nonnull complex sample covariance matrices in a recent study of large non null sample covariance matrices a new sequence of functions gener alizing the gue tracy widom distribution of random matrix theory was obtained this paper derives painleve formulas of these functions and use them to prove that they are indeed distribution functions applications of these new distribution functions to last passage percolation queues in tandem and to tally asymmetric simple exclusion process are also discussed as a part of the proof a representation of orthogonal polynomials on the unit circle in terms of an operator on a discrete set is presented

asymptotic periodicity for some evolution equations in banach spaces abstract this work deals with the existence and uniqueness of pseudo almost periodic and asymptotically periodic mild solutions to some evolution equations in banach spaces

asymptotic periodicity for hyperbolic evolution equations and applications we study the existence and uniqueness of pseudo s asymptotically periodic mild solutions for hyperbolic evolution equations we show concrete applications of our methods

the problem of harmonic analysis on the infinite dimensional unitary group abstract the goal of harmonic analysis on a noncommutative group is to decompose the most natural unitary representations of this group like the regular representation on irreducible ones the infinite dimensional unitary group u is one of the basic examples of big groups whose irreducible representations depend on infinitely many parameters our aim is to explain what the harmonic analysis on u consists of we deal with unitary representations of a reasonable class which are in 1 1 correspondence with characters central positive definite normalized functions on u the decomposition of any representation of this class is described by a probability measure called spectral measure on the space of indecomposable characters the indecomposable characters were found by dan voiculescu in 1976 the main result of the present paper consists in explicitly constructing a 4 parameter family of natural representations and computing their characters we view these representations as a substitute of the nonexisting regular representation of u we state the problem of harmonic analysis on u as the problem of computing the spectral measures for these natural representations a solution to this problem is given in the next paper harmonic analysis on the infinite dimensional unitary group and determinantal point processes math 0109194 to appear in ann math joint with alexei borodin we also prove a few auxiliary general results in particular it is proved that the spectral measure of any character of u can be approximated by a sequence of discrete spectral measures for the restrictions of the character to the compact unitary groups u n this fact is a starting point for computing spectral measures

asymptotics of plancherel type random partitions abstract we present a solution to a problem suggested by philippe biane we prove that a certain plancherel type probability distribution on partitions converges as partitions get large to a new determinantal random point process on the set z of nonnegative integers this can be viewed as an edge limit transition the limit process is determined by a correlation kernel on z which is expressed through the hermite polynomials we call it the discrete hermite kernel the proof is based on a simple argument which derives convergence of correlation kernels from convergence of unbounded self adjoint difference operators our approach can also be applied to a number of other probabilistic models as an example we discuss a bulk limit for one more plancherel type model of random partitions

asymptotically periodic solutions of fractional differential equations abstract we study the existence of pseudo s asymptotically periodic mild solutions for a class of abstract fractional differential equation

quasi symmetries of determinantal point processes the main result of this paper is that determinantal point processes on mathbb r corresponding to projection operators with integrable kernels are quasi invariant in the continuous case under the group of diffeomorphisms with compact support theorem 1 4 in the discrete case under the group of all finite permutations of the phase space theorem 1 6 the radon nikodym derivative is computed explicitly and is given by a regularized multiplicative functional theorem 1 4 applies in particular to the sine process as well as to determinantal point processes with the bessel and the airy kernels theorem 1 6 to the discrete sine process and the gamma kernel process the paper answers a question of grigori olshanski

asymptotic values for degrees associated with strips of young diagrams abstract the sums s l n occur in the representations of the symmetric and the general linear groups in combinatorics and in pi algebras we give asymptotic values for these sums

a fredholm determinant identity and the convergence of moments for random young tableaux we obtain an identity between fredholm determinants of two kinds of operators one acting on functions on the unit circle and the other acting on functions on a subset of the integers this identity is a generalization of an identity between a toeplitz determinant and a fredholm determinant that has appeared in the random permutation context using this identity we prove in particular convergence of moments for arbitrary rows of a random young diagram under plancherel measure

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

hammersley s interacting particle process and longest increasing subsequences in a famous paper 8 hammersley investigated the lengthl n of the longest increasing subsequence of a randomn permutation implicit in that paper is a certain one dimensional continuous space interacting particle process by studying a hydrodynamical limit for hammersley s process we show by fairly soft arguments that limn 1 2 el n 2 this is a known result but previous proofs 14 11 relied on hard analysis of combinatorial asymptotics

existence of mild solutions for fractional integrodifferential equations of sobolev type with nonlocal conditions abstract this paper is concerned with the fractional integrodifferential equations of sobolev type with nonlocal condition in a separable banach space with the help of the theory of propagation family as well as the theory of the measures of noncompactness and the condensing maps we obtain the existence result of mild solutions for above equations two examples are given to illustrate the existence theorem

random point fields associated with certain fredholm determinants i fermion poisson and boson point processes we introduce certain classes of random point fields including fermion and boson point processes which are associated with fredholm determinants of certain integral operators and study some of their basic properties limit theorems correlation functions palm measures etc also we propose a conjecture on an analogue of the determinant and permanent

on a conjecture of widom we prove a conjecture of widom 2002 int math res not 455 64 preprint math 0108008 about the reality of eigenvalues of certain infinite matrices arising in asymptotic analysis of large toeplitz determinants as a byproduct we obtain a new proof of okounkov s formula for the determinantal correlation functions of the schur measures on partitions

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

existence results for fractional neutral integro differential equations with state dependent delay in this paper we study the existence of mild solutions for a class of abstract fractional neutral integro differential equations with state dependent delay the results are obtained by using the leray schauder alternative fixed point theorem an example is provided to illustrate the main results

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

large deformations of the tracy widom distribution i non oscillatory asymptotics we analyze the left tail asymptotics of deformed tracy widom distribution functions describing the fluctuations of the largest eigenvalue in invariant random matrix ensembles after removing each soft edge eigenvalue independently with probability 1 gamma in 0 1 as gamma varies a transition from tracy widom statistics gamma 1 to classical weibull statistics gamma 0 was observed in the physics literature by bohigas et al phys rev e 79 031117 2009 we provide a description of this transition by rigorously computing the leading order left tail asymptotics of the thinned goe gue and gse tracy widom distributions in this paper we obtain the asymptotic behavior in the non oscillatory region with gamma in 0 1 fixed for the goe gue and gse distributions and gamma uparrow 1 at a controlled rate for the gue distribution this is the first step in an ongoing program to completely describe the transition between tracy widom and weibull statistics as a corollary to our results we obtain a new total integral formula involving the ablowitz segur solution to the second painleve equation