Related papers: Matrix Kesten Recursion, Inverse-Wishart Ensemble …

Let $\a$ be a complex random variable with mean zero and bounded variance $\sigma^{2}$. Let $N_{n}$ be a random matrix of order $n$ with entries being i.i.d. copies of $\a$. Let $\lambda_{1}, ..., \lambda_{n}$ be the eigenvalues of…

Let $N(L)$ be the number of eigenvalues, in an interval of length $L$, of a matrix chosen at random from the Gaussian Orthogonal, Unitary or Symplectic ensembles of ${\cal N}$ by ${\cal N}$ matrices, in the limit ${\cal…

In this article, we study high-dimensional behavior of empirical spectral distributions $\{L_N(t), t\in[0,T]\}$ for a class of $N\times N$ symmetric/Hermitian random matrices, whose entries are generated from the solution of stochastic…

In the customary random matrix model for transport in quantum dots with $M$ internal degrees of freedom coupled to a chaotic environment via $N\ll M$ channels, the density $\rho$ of transmission eigenvalues is computed from a specific…

We consider a finite collection of independent Hermitian heavy-tailed random matrices of growing dimension. Our model includes the L\'evy matrices proposed by Bouchaud and Cizeau, as well as sparse random matrices with O(1) non-zero entries…

We consider a $p$-dimensional time series where the dimension $p$ increases with the sample size $n$. The resulting data matrix $X$ follows a stochastic volatility model: each entry consists of a positive random volatility term multiplied…

We study the eigenvalue correlations of random Hermitian $n\times n$ matrices of the form $S=M+\epsilon H$, where $H$ is a GUE matrix, $\epsilon>0$, and $M$ is a positive-definite Hermitian random matrix, independent of $H$, whose…

We consider $N\times N$ symmetric or hermitian random matrices with independent, identically distributed entries where the probability distribution for each matrix element is given by a measure $\nu$ with a subexponential decay. We prove…

We compute exact asymptotic of the statistical density of random matrices belonging to the Generalized Gaussian orthogonal, unitary and symplectic ensembles such that there no eigenvalues in the interval $[\sigma, +\infty[$. In particular,…

The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are…

In this paper, we study tail inequalities of the largest eigenvalue of a matrix infinitely divisible (i.d.) series, which is a finite sum of fixed matrices weighted by i.d. random variables. We obtain several types of tail inequalities,…

We characterize the phenomenon of "crowding" near the largest eigenvalue $\lambda_{\max}$ of random $N \times N$ matrices belonging to the Gaussian $\beta$-ensemble of random matrix theory, including in particular the Gaussian orthogonal…

For a large class of random matrices $A$ with i.i.d. entries we show that the $\ell_1$-quotient property holds with probability exponentially close to 1. In contrast to previous results, our analysis does not require concentration of the…

One-rank perturbations of Wigner matrices have been closely studied: let $P=\frac{1}{\sqrt{n}}A+\theta vv^T$ with $A=(a_{ij})_{1 \leq i,j \leq n} \in \mathbb{R}^{n \times n}$ symmetric, $(a_{ij})_{1 \leq i \leq j \leq n}$ i.i.d. with…

Recently, we have classified Hermitian random matrix ensembles that are invariant under the conjugate action of the unitary group and stable with respect to matrix addition. Apart from a scaling and a shift, the whole information of such an…

In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…

Joint distribution function of N eigenvalues of U(N) invariant random-matrix ensemble can be interpreted as a probability density to find N fictitious non-interacting fermions to be confined in a one-dimensional space. Within this picture a…

We show that an independent family of uniformly distributed random permutation matrices is asymptotically *-free from an independent family of square complex Gaussian matrices and from an independent family of complex Wishart matrices, and…

Random matrix theory has become a cornerstone in modern statistics and data science, providing fundamental tools for understanding high-dimensional covariance structures. Within this framework, the Wishart matrix plays a central role in…

We study an unconventional chiral random matrix model with a heavy-tailed probabilistic weight. The model is shown to exhibit chiral symmetry breaking with no bilinear condensate, in analogy to the Stern phase of QCD. We solve the model…