stabilization of nonlinear systems via forwarding mod l sub g v forwarding is a tool for constructing stabilizers for nonlinear systems a key step in this design technique is to find an explicit solution to a partial differential equation pde which may be hard to find actually the pde may even not be solvable at all in this paper we show that it is possible to provide an additional degree of freedom for the solution of the aforementioned pde hence effectively extending the realm of application of the forwarding methodology our contribution is illustrated with the example of an inverted pendulum with a disk inertia

on the characteristic polynomial of a random unitary matrix we present a range of fluctuation and large deviations results for the logarithm of the characteristic polynomial z of a random n n unitary matrix as n first we show that evaluated at a finite set of distinct points is asymptotically a collection of i i d complex normal random variables this leads to a refinement of a recent central limit theorem due to keating and snaith and also explains the covariance structure of the eigenvalue counting function next we obtain a central limit theorem for ln z in a sobolev space of generalised functions on the unit circle in this limiting regime lower order terms which reflect the global covariance structure are no longer negligible and feature in the covariance structure of the limiting gaussian measure large deviations results for ln z a evaluated at a finite set of distinct points can be obtained for for higher order scalings we obtain large deviations results for ln z a evaluated at a single point there is a phase transition at a ln n which only applies to negative deviations of the real part reflecting a switch from global to local conspiracy

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

level spacing distributions and the bessel kernel scaling models of randomn n hermitian matrices and passing to the limitn leads to integral operators whose fredholm determinants describe the statistics of the spacing of the eigenvalues of hermitian matrices of large order for the gaussian unitary ensemble and for many others as well the kernel one obtains by scaling in the bulk of the spectrum is the sine kernel frac sin pi x y pi x y rescaling the gue at the edge of the spectrum leads to the kernel frac ai x ai y ai x ai y x y where ai is the airy function in previous work we found several analogies between properties of this airy kernel and known properties of the sine kernel a system of partial differential equations associated with the logarithmic differential of the fredholm determinant when the underlying domain is a union of intervals a representation of the fredholm determinant in terms of a painleve transcendent in the case of a single interval and also in this case asymptotic expansions for these determinants and related quantities achieved with the help of a differential operator which commutes with the integral operator in this paper we show that there are completely analogous properties for a class of kernels which arise when one rescales the laguerre or jacobi ensembles at the edge of the spectrum namely frac j alpha sqrt x sqrt y j alpha sqrt y sqrt x j alpha sqrt x j alpha sqrt y 2 x y wherej z is the bessel function of order in the cases 1 2 these become after a variable change the kernels which arise when taking scaling limits in the bulk of the spectrum for the gaussian orthogonal and symplectic ensembles in particular an asymptotic expansion we derive will generalize ones found by dyson for the fredholm determinants of these kernels

level spacings distribution for large random matrices gaussian fluctuations we study the level spacings distribution for eigenvalues of large n x n matrices from the classical compact groups in the scaling limit when the mean distance between nearest eigenvalues equals 1 defining by 77n s the number of nearest neighbors spacings greater than s 0 smaller than s 0 we prove functional limit theorem for the process 77n s e n s n1 2 giving weak convergence of this distribution to some gaussian random process on 0 x the limiting gaussian random process is universal for all classical compact groups it is holder continuous with any exponent less than 1 2 similar results can be obtained for the n level spacings distribution

interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

gaussian fluctuations of young diagrams under the plancherel measure we obtain the central limit theorem for fluctuations of young diagrams around their limit shape in the bulk of the spectrum of partitions lwn2n under the plancherel measure thus settling a long standing problem posed by logan shepp namely under normalization growing like ffiffiffiffiffiffiffiffiffiffiffi n p the corresponding random process in the bulk is shown to converge in the sense of finite dimensional distributions to a gaussian process with independent values while local correlations in the vicinity of each point measured on various power scales possess certain self similarity the proofs are based on the poissonization techniques and use costin lebowitz soshnikov s central limit theorem for determinantal random point processes our results admit a striking reformulation after the rotation of young diagrams by 458 whereby the normalization no longer depends on the location in the spectrum in addition we explain heuristically the link with an earlier result by kerov on the convergence to a generalized gaussian process

stabilization of hamiltonian systems with nonholonomic constraints based on time varying generalized canonical transformations this paper is concerned with the stabilization of nonholonomic systems in port controlled hamiltonian formulae based on time varying generalized canonical transformations a special class of time varying generalized canonical transformations are introduced which modify the kinetic energy of the original system without changing the generalized hamiltonian structure with passivity utilizing these transformations time varying asymptotically stabilizing controllers for the nonholonomic hamiltonian systems are derived since the proposed method is a natural generalization of passivity based control for conventional holonomic systems it is expected that the tools developed for conventional systems will be applicable to nonholonomic systems based on the proposed method

on pfaffian random point fields we study pfaffian random point fields by using the moore dyson quaternion determinants first we give sufficient conditions that ensure that a self dual quaternion kernel defines a valid random point field and then we prove a clt for pfaffian point fields the proofs are based on a new quaternion extension of the cauchy binet determinantal identity in addition we derive the fredholm determinantal formulas for the pfaffian point fields which use the quaternion determinant

the matching conditions of controlled lagrangians and ida passivity based control this paper discusses the matching conditions resulting from the controlled lagrangians method and the interconnection and damping assignment passivity based control ida pbc method both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an euler lagrange respectively hamiltonian system in the context of mechanical systems with symmetry the original controlled lagrangians method is reviewed and an interpretation of the matching assumptions in terms of the matching of kinetic and potential energy is given secondly both methods are applied to the general class of underactuated mechanical systems and it is shown that the controlled lagrangians method is contained in the ida pbc method the lambda method as described in recent papers for the controlled lagrangians method transforming the matching conditions a set of non linear pdes into a set of linear pdes is discussed the method is used to transform the matching conditions obtained in the ida pbc method into a set of quadratic and linear pdes finally the extra freedom obtained in the ida pbc method with respect to the controlled lagrangians method is used to discuss the integrability of the closed loop system explicit conditions are derived under which the closed loop hamiltonian system is integrable leading to the introduction of gyroscopic terms

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

finite n fluctuation formulas for random matrices for the gaussian and laguerre random matrix ensembles the probability density function p d f for the linear statistic jn 1 xj x is computed exactly and shown to satisfy a central limit theorem asn for the circular random matrix ensemble the p d f s for the statistics jn 1 j and jn 1 log 2 sin j 2 are calculated exactly by using a constant term identity from the theory of the selberg integral and are also shown to satisfy a central limit theorem asn

universality of local eigenvalue statistics for some sample covariance matrices we consider random complex sample covariance matrices 1 x x where x is a p n random matrix with i i d entries of distribution it has been conjectured that both the distribution of the distance between nearest neighbor eigenva lues in the bulk and that of the smallest eigenvalues become in the limit n p n 1 the same as that identified for a complex gaussian distribution we prove these conjectures for a certain class of probability distributions c 2004 wiley periodicals inc

stabilization of a class of underactuated mechanical systems via interconnection and damping assignment we consider the application of a formulation of passivity based control pbc known as interconnection and damping assignment ida to the problem of stabilization of underactuated mechanical systems which requires the modification of both the potential and the kinetic energies our main contribution is the characterization of a class of systems for which ida pbc yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction the class is given in terms of solvability of certain partial differential equations one important feature of ida pbc stemming from its hamiltonian formulation is that it provides new degrees of freedom for the solution of these equations using this additional freedom we are able to show that the method of controlled lagrangians in its original formulation may be viewed as a special case of our approach as illustrations we design asymptotically stabilizing ida pbcs for the classical ball and beam system and a novel inertia wheel pendulum

quadratic pairs without commuting root subgroups abstract suppose g is a subgroup of gl k m a finite dimensional vectorspace over the field k with char k 2 generated by quadratic elements satisfying c g for all c k then one can define root subgroups of g intrinsically i e just in terms of the quadratic elements in this paper we determine such groups g generated by three root subgroups which do not contain a pair of commuting root subgroups this is a further step of the determination of groups g when g m is a quadratic pair

transversal fluctuations for increasing subsequences on the plane consider a realization of a poisson process in 2 with intensity 1 and take a maximal up right path from the origin to n n consisting of line segments between the points where maximal means that it contains as many points as possible the number of points in such a path has fluctuations of order n where 1 3 bdj here we show that typical deviations of a maximal path from the diagonal x y is of order n with 2 3 this is consistent with the scaling identity 2 1 which is believed to hold in many random growth models

central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients we study fluctuations of linear statistics corresponding to smooth functions for certain biorthogonal ensembles we study those biorthogonal ensembles for which the underlying biorthogonal family s

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

deviations from the circular law consider ginibre s ensemble of n n non hermitian random matrices in which all entries are independent complex gaussians of mean zero and variance open image in new window as n the normalized counting measure of the eigenvalues converges to the uniform measure on the unit disk in the complex plane in this note we describe fluctuations about this circular law first we obtain finite n formulas for the covariance of certain linear statistics of the eigenvalues asymptotics of these objects coupled with a theorem of costin and lebowitz then result in central limit theorems for a variety of these statistics

the local circular law ii the edge case in the first part of this article bourgade et al arxiv 1206 1449 2012 we proved a local version of the circular law up to the finest scale n 1 2 varepsilon for non hermitian random matrices at any point z in mathbb c with z 1 c for any c 0 independent of the size of the matrix under the main assumption that the first three moments of the matrix elements match those of a standard gaussian random variable after proper rescaling we extend this result to include the edge case z 1 mathrm o 1 without the vanishing third moment assumption we prove that the circular law is valid near the spectral edge z 1 mathrm o 1 up to scale n 1 4 varepsilon

dynamic extension is unnecessary for stabilization via interconnection and damping assignment passivity based control interconnection and damping assignment passivity based control ida pbc is a technique that regulates the behavior of nonlinear systems assigning a desired port hamiltonian structure to the closed loop this basic idea introduced seven years ago has turned out to be very successful and has provided solutions to a wide variety of physical problems although ida pbc is originally formulated as a static state feedback technique a natural question that arises is whether it is possible to extend the realm of applicability of the method by considering dynamic controllers more precisely is the set of plants that is stabilizable with static state feedback ida pbc smaller than the one stabilizable with dynamic ida pbc the main contribution of this paper is to prove that the answer to this question is unfortunately negative

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

determinants of airy operators and applications to random matrices the purpose of this paper is to describe asymptotic formulas for determinants of certain operators that are analogues of wiener hopf operators the determinant formulas yield information about the distribution functions for certain random variables that arise in random matrix theory when one rescales at the edge of the spectrum

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

distribution functions for random variables for ensembles of positive hermitian matrices distribution functions for random variables that depend on a parameter are computed asymptotically for ensembles of positive hermitian matrices the inverse fourier transform of the distribution is shown to be a fredholm determinant of a certain operator that is an analogue of a wiener hopf operator the asymptotic formula shows that up to the terms of order o 1 the distributions are gaussian

bounded stabilisation of stochastic port hamiltonian systems this paper proposes a stochastic bounded stabilisation method for a class of stochastic port hamiltonian systems both full actuated and underactuated mechanical systems in the presence of noise are considered in this class the proposed method gives conditions for the controller gain and design parameters under which the state remains bounded in probability the bounded region and achieving probability are both assignable and a stochastic lyapunov function is explicitly provided based on a hamiltonian structure although many conventional stabilisation methods assume that the noise vanishes at the origin the proposed method is applicable to systems under persistent disturbances

universality at the edge of the spectrum in wigner random matrices we prove universality at the edge for rescaled correlation functions of wigner random matrices in the limit n as a corollary we show that after proper rescaling the 1th 2nd 3rd etc eigenvalues of wigner random hermitian resp real symmetric matrix weakly converge to the distributions established by tracy and widom in g u e g o e cases

large deviations for the fermion point process associated with the exponential kernel for the fermion point process on the whole complex plane associated with the exponential kernel e z bar w we show the central limit theorem for the random variable d r the number of points inside the ball d r of radius r as r and we establish the large deviation principle for the random variables r 2 d r r 0

on the lambda equations for matching control laws we discuss matching control laws for underactuated systems we previously showed that this class of matching control laws is completely characterized by a linear system of first order partial differential equations for one set of variables lambda followed by a linear system of first order partial differential equations for the second set of variables widehat g widehat v here we derive a new first order system of partial differential equations that encodes all compatibility conditions for the lambda equations we give four examples illustrating different features of matching control laws the last example is a system with two unactuated degrees of freedom that admits only basic solutions to the matching equations there are systems with many matching control laws where only basic solutions are potentially useful we introduce a rank condition indicating when this is likely to be the case

nonlinear control via approximate input output linearization the ball and beam example approximate input output linearization of nonlinear systems which fail to have a well defined relative degree is studied for such systems a method for constructing approximate systems that are input output linearizable is provided the analysis presented is motivated through its application to a common undergraduate control laboratory experiment the ball and beam where it is shown to be more effective for trajectory tracking than the standard jacobian linearization

the central limit theorem for local linear statistics in classical compact groups and related combinatorial identities author s soshnikov alexander abstract we discuss clt for the global and local linear statistics of random matrices from classical compact groups the main part of our proofs are certain combinatorial identities much in the spirit of works by kac and spohn

controlled lagrangians and the stabilization of mechanical systems i the first matching theorem we develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled lagrangians the procedure involves making structured modifications to the lagrangian for the uncontrolled system thereby constructing the controlled lagrangian the euler lagrange equations derived from the controlled lagrangian describe the closed loop system where new terms in these equations are identified with control forces since the controlled system is lagrangian by construction energy methods can be used to find control gains that yield closed loop stability we use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group the procedure is demonstrated for several underactuated balance problems including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane

local central limit theorem for determinantal point processes we prove a local central limit theorem lclt for the number of points n j in a region j in mathbb r d specified by a determinantal point process with an hermitian kernel the only assumption is that the variance of n j tends to infinity as j rightarrow infty this extends a previous result giving a weaker central limit theorem for these systems our result relies on the fact that the lee yang zeros of the generating function for e k j the probabilities of there being exactly k points in j all lie on the negative real z axis in particular the result applies to the scaled bulk eigenvalue distribution for the gaussian unitary ensemble gue and that of the ginibre ensemble for the gue we can also treat the properly scaled edge eigenvalue distribution using identities between gap probabilities the lclt can be extended to bulk eigenvalues of the gaussian symplectic ensemble a lclt is also established for the probability density function of the k th largest eigenvalue at the soft edge and of the spacing between k th neighbors in the bulk

universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles this paper is devoted to the rigorous proof of the universality conjecture of random matrix theory according to which the limiting eigenvalue statistics ofn n random matrices within spectral intervals ofo n 1 is determined by the type of matrix real symmetric hermitian or quaternion real and by the density of states we prove this conjecture for a certain class of the hermitian matrix ensembles that arise in the quantum field theory and have the unitary invariant distribution defined by a certain function the potential in the quantum field theory satisfying some regularity conditions

zeros of the i i d gaussian power series a conformally invariant determinantal process consider the zero set of the random power series f z p anz n with i i d complex gaussian coefficientsan we show that these zeros form a determinantal process more precisely their joint intensity can be written as a minor of the bergman kernel we show that the number of zeros of f in a disk of radius r about the origin has the same distribution as the sum of independent 0 1 valued random variables xk where p xk 1 r 2k moreover the set of absolute values of the zeros of f has the

on eigenvalues of the sum of two random projections we study the behavior of eigenvalues of matrix p n q n where p n and q n are two n by n random orthogonal projections we relate the joint eigenvalue distribution of this matrix to the jacobi matrix ensemble and establish the universal behavior of eigenvalues for large n the limiting local behavior of eigenvalues is governed by the sine kernel in the bulk and by either the bessel or the airy kernel at the edge depending on parameters we also study an exceptional case when the local behavior of eigenvalues of p n q n is not universal in the usual sense

gaussian fluctuations of eigenvalues in wigner random matrices we study the fluctuations of eigenvalues from a class of wigner random matrices that generalize the gaussian orthogonal ensemble we begin by considering an n n matrix from the gaussian orthogonal ensemble goe or gaussian symplectic ensemble gse and let xk denote eigenvalue number k under the condition that both k and n k tend to infinity as n w e show thatxk is normally distributed in the limit we also consider the joint limit distribution of eigenvalues xk1 x km from the goe or gse where k1 n km and ki 1 ki 1 i m 1 tend to infinity with n the result in each case is an m dimensional normal distribution using a recent universality result by tao and vu we extend our results to a class of wigner real symmetric matrices with non gaussian entries that have an exponentially de caying distribution and whose first four moments match the gaussian moments

semiclassical asymptotics of orthogonal polynomials riemann hilbert problem and universality in the matrix model we derive semiclassical asymptotics for the orthogonal polynomials pn z on the line with respect to the exponential weight exp inv z where v z is a double well quartic polynomial in the limit when n n 1 we assume that n n cri for some 0 where cr is the critical value which separates orthogonal polynomials with two cuts from the ones with one cut simultaneously we derive semiclassical asymptotics for the recursive coe cients of the orthogonal polynomials and we show that these coe cients form a cycle of period two which drifts slowly with the change of the ratio n n the proof of the semiclassical asymptotics is based on the methods of the theory of integrable systems and on the analysis of the appropriate matrix riemannhilbert problem as an application of the semiclassical asymptotics of the orthogonal polynomials we prove the universality of the local distribution of eigenvalues in the matrix model with the double well quartic interaction in the presence of two cuts contents

dynamics and control of a class of underactuated mechanical systems this paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems defined as systems with fewer inputs than degrees of freedom control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified controllability and stabilizability results are derived for this class of underactuated systems examples are included to illustrate the results these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable

control of nonlinear underactuated systems in this paper we introduce a new method to design control laws for nonlinear underactuated systems our method produces an infinite dimensional family of control laws whereas most control techniques only produce a finite dimensional family these control laws each come with a natural lyapunov function the inverted pendulum cart is used as an example in addition we construct an abstract system that is open loop unstable and cannot be stabilized using any linear control law and demonstrate that our method produces a stabilizing control law 2000 john wiley sons inc

lower tail of the kpz equation we provide the first tight bounds on the lower tail probability of the one point distribution of the kardar parisi zhang kpz equation with narrow wedge initial data our bounds hold for all sufficiently large times t and demonstrates a crossover between superexponential decay with exponent 52 and leading prefactor 415 t1 3 for tail depth greater than t2 3 and exponent 3 with leading prefactor at least 112 for tail depth less than t2 3

normal approximation for associated point processes via stein s method with applications to determinantal point processes abstract we use stein s method to provide non asymptotic l 1 bounds also known as wasserstein bounds to the normal for functionals of associated point processes as for supporting tools we use the connection between association and mixing properties that was recently uncovered by 29 we apply our main results to determinantal point processes which are known to be negatively associated a potential application to determinantal point processes in the laguerre gaussian family is also presented

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

stabilization lyapunov functions and dissipation for linear time invariant systems any stabilizing controller for a given plant can be associated with a supply rate with respect to which the plant in open loop is half line dissipative we also prove the equivalence between the stability of the interconnection of two systems and their half line dissipativity with respect to a supply rate and its negative

random point fields associated with certain fredholm determinants ii fermion shifts and their ergodic and gibbs properties we construct and study a family of probability measures on the configuration space over countable discrete space associated with nonnegative definite symmetric operators via determinants under a mild condition they turn out unique gibbs measures also some ergodic properties including the entropy positivity are discussed in the lattice case

stabilization of systems with one degree of underactuation with energy shaping a geometric approach a geometric formulation for stabilization of systems with one degree of underactuation which fully solves the energy shaping problem for these system is given the results show that any linearly controllable simple mechanical system with one degree of underactuation is stabilizable by energy shaping even in the absence of gyroscopic force via a closed loop metric which is not necessarily positive definite an example of a system with one degree of underactuation is provided for which the stabilization by energy shaping method is not achievable in the absence of gyroscopic forces using a positive definite closed loop metric

on fluctuations of riemann s zeta zeros it is shown that the normalized fluctuations of riemann s zeta zeros around their predicted locations follow the gaussian law it is also shown that fluctuations of two zeros gamma k and gamma k x with x sim left log k right beta beta 0 for large k follow the two variate gaussian distribution with correlation left 1 beta right

asymptotic properties of large random matrices with independent entries we study the normalized trace gn z n 1 tr h zi 1 of the resolvent of n n real symmetric matrices h 1 jk wjk n j k 1n assuming that their entries are independent but not necessarily identically distributed random variables we develop a rigorous method of asymptotic analysis of moments of gn z for iz 0 where 0 is determined by the second moment of wjk by using this method we find the asymptotic form of the expectation e gn z and of the connected correlator e gn z1 gn z2 e gn z1 e gn z2 we also prove that the centralized trace ngn z e ngn z has the gaussian distribution in the limit n based on these results we present heuristic arguments supporting the universality property of the local eigenvalue statistics for this class of random matrix ensembles

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