Related papers: On the eigenvalues of truncations of random unitar…

We determine the limiting empirical singular value distribution for random unitary matrices with Haar distribution and discrete Fourier transform (DFT) matrices when a random set of columns and rows is removed.

Denote by $\lambda_1(A), \ldots, \lambda_n(A)$ the eigenvalues of an $(n\times n)$-matrix $A$. Let $Z_n$ be an $(n\times n)$-matrix chosen uniformly at random from the matrix analogue to the classical $\ell_ p^n$-ball, defined as the set of…

Let $f=(f_1,\ldots,f_n)$ be a system of $n$ complex homogeneous polynomials in $n$ variables of degree $d$. We call $\lambda\in\mathbb{C}$ an eigenvalue of $f$ if there exists $v\in\mathbb{C}^n\backslash\{0\}$ with $f(v)=\lambda v$,…

We investigate the Brenier map $\nabla \Phi$ between the uniform measures on two convex domains in $\mathbb{R}^n$ or more generally, between two log-concave probability measures on $\mathbb{R}^n$. We show that the eigenvalues of the Hessian…

This paper investigates local spectral statistics of singular values for many products of independent large rectangular matrices, sampled from the ensemble of truncated unitary matrices with the invariant Haar measure. Our main contribution…

A spectral average which generalises the local spacing distribution of the eigenvalues of random $ N\times N $ hermitian matrices in the bulk of their spectrum as $ N\to\infty $ is known to be a $\tau$-function of the fifth Painlev\'e…

For fixed $l,m \ge 1$, let $\mathbf{X}_n^{(0)},\mathbf{X}_n^{(1)},\dots,\mathbf{X}_n^{(l)}$ be independent random $n \times n$ matrices with independent entries, let $\mathbf{F}_n^{(0)} := \mathbf{X}_n^{(0)} (\mathbf{X}_n^{(1)})^{-1} \cdots…

We consider the ensemble of $N\times N$ real random symmetric matrices $H_N^{(R)}$ obtained from the determinant form of the Ihara zeta function associated to random graphs $\Gamma_N^{(R)}$ of the long-range percolation radius model with…

We consider a class of random banded Hessenberg matrices with independent entries having identical distributions along diagonals. The distributions may be different for entries belonging to different diagonals. For a sequence of $n\times n$…

The optimal transport map between the standard Gaussian measure and an $\alpha$-strongly log-concave probability measure is $\alpha^{-1/2}$-Lipschitz, as first observed in a celebrated theorem of Caffarelli. In this paper, we apply two…

We give an upper bound on the total variation distance between the linear eigenvalue statistic, properly scaled and centred, of a random matrix with a variance profile and the standard Gaussian random variable. The second order Poincar\'e…

Let \{$X_{ij}$\}, $i,j=...,$ be a double array of i.i.d. complex random variables with $EX_{11}=0,E|X_{11}|^2=1$ and $E|X_{11}|^4<\infty$, and let $A_n=\frac{1}{N}T_n^{{1}/{2}}X_nX_n^*T_n^{{1}/{2}}$, where $T_n^{{1}/{2}}$ is the square root…

In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter $\theta>0$) by replacing the entries equal to one by…

We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…

We study the eigenvalues of a Laplace-Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. By assigning partitions with the restricted uniform measure,…

We study the statistical properties of eigenvalues of the Hessian matrix ${\cal H}$ (matrix of second derivatives of the potential energy) for a classical atomic liquid, and compare these properties with predictions for random matrix models…

Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…

Consider the product of $m$ independent $n\times n$ random matrices from the spherical ensemble for $m\ge 1$. The spectral radius is defined as the maximum absolute value of the $n$ eigenvalues of the product matrix. When $m=1$, the…

This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly…

We consider $N\times N$ Hermitian or symmetric random matrices with independent entries. The distribution of the $(i,j)$-th matrix element is given by a probability measure $\nu_{ij}$ whose first two moments coincide with those of the…