相关论文: Borel theorems for random matrices from the classi…

We compute the rational Borel-Moore homology groups for affine determinantal varieties in the spaces of general, symmetric, and skew-symmetric matrices, solving a problem suggested by the work of Pragacz and Ratajski. The main ingredient is…

A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realised by matrices with Gaussian entries leads to statistical quantities…

A known result in random matrix theory states the following: Given a random Wigner matrix $X$ which belongs to the Gaussian Orthogonal Ensemble (GOE), then such matrix $X$ has an invariant distribution under orthogonal conjugations. The…

Correlation functions involving products and ratios of half-integer powers of characteristic polynomials of random matrices from the Gaussian Orthogonal Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT) to…

We introduce an alternative combinatorial parametrization of Borel orbits in classical symmetric varieties using matchings of the Corona graph. As an application, we obtain ultra log-concavity and unimodality for the number of Borel orbits…

We complete Dyson's dream by cementing the links between symmetric spaces and classical random matrix ensembles. Previous work has focused on a one-to-one correspondence between symmetric spaces and many but not all of the classical random…

Toral automorphisms, represented by unimodular integer matrices, are investigated with respect to their symmetries and reversing symmetries. We characterize the symmetry groups of GL(n,Z) matrices with simple spectrum through their…

Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate…

Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class…

A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally…

A connection between representation of compact groups and some invariant ensembles of Hermitian matrices is described. We focus on two types of invariant ensembles which extend the Gaussian and the Laguerre Unitary ensembles. We study them…

This paper considers the empirical spectral measure of a power of a random matrix drawn uniformly from one of the compact classical matrix groups. We give sharp bounds on the $L_p$-Wasserstein distances between this empirical measure and…

On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure,…

We consider the space $\mathcal{D}'^r_L(M;E)$ of distributional sections of the smooth complex vector bundle $E\rightarrow M$ whose Sobolev wave front set of order $r\in\mathbb{R}$ lies in the closed conic subset $L$ of $T^*M\backslash0$.…

In this paper, we are interested in sequences of q-tuple of N-by-N random matrices having a strong limiting distribution (i.e. given any non-commutative polynomial in the matrices and their conjugate transpose, its normalized trace and its…

Rudnick recently proved that the spectral number variance for the Laplacian of a large compact hyperbolic surface converges, in a certain scaling limit and when averaged with respect to the Weil-Petersson measure on moduli space, to the…

Let G be a semisimple linear algebraic group defined over rational numbers, K be a maximal compact subgroup of its real points and {\Gamma} be an arithmetic lattice. One can associate a probability measure {\mu}(H) on {\Gamma}\G for each…

We consider a class of sample covariance matrices of the form $Q=TXX^{*}T^*,$ where $X=(x_{ij})$ is an $M \times N$ rectangular matrix consisting of i.i.d entries and $T$ is a deterministic matrix satisfying $T^*T$ is diagonal. Assuming $M$…

Let $\Gamma$ be a countable group. A classical theorem of Thorisson states that if $X$ is a standard Borel $\Gamma$-space and $\mu$ and $\nu$ are Borel probability measures on $X$ which agree on every $\Gamma$-invariant subset, then $\mu$…

Let A be a standard Borel space, and consider the space A^{\bbN^{(k)}} of A-valued arrays indexed by all size-k subsets of \bbN. This paper concerns random measures on such a space whose laws are invariant under the natural action of…