Related papers: Universality and sharp matrix concentration inequa…

We consider matrix-valued processes described as solutions to stochastic differential equations of very general form. We study the family of the empirical measure-valued processes constructed from the corresponding eigenvalues. We show that…

Let $M_n = (\xi_{ij})_{1 \leq i,j \leq n}$ be a real symmetric random matrix in which the upper-triangular entries $\xi_{ij}, i<j$ and diagonal entries $\xi_{ii}$ are independent. We show that with probability tending to 1, $M_n$ has no…

Matrix concentration inequalities provide information about the probability that a random matrix is close to its expectation with respect to the $l_2$ operator norm. This paper uses semigroup methods to derive sharp nonlinear matrix…

The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of…

Applying the concept of matricial freeness which generalizes freeness in free probability, we have recently studied asymptotic joint distributions of symmetric blocks of Gaussian random matrices (Gaussian Symmetric Block Ensemble). This…

We extend a recent theory of parametric correlations in the spectrum of random matrices to study the response to an external perturbation of eigenvalues near the soft edge of the support. We demonstrate by explicit non-perturbative…

We present progress on the problem of asymptotically describing the adjacency eigenvalues of random and complete uniform hypergraphs. There is a natural conjecture arising from analogy with random matrix theory that connects these spectra…

This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…

Let $U_n$ be an $n \times n$ Haar unitary matrix. In this paper, the asymptotic normality and independence of $\Tr U_n, \Tr U_n^2, ..., \Tr U_n^k$ are shown by using elementary methods. More generally, it is shown that the renormalized…

This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav…

We study ensembles of sparse random block matrices generated from the adjacency matrix of a Erd\"os-Renyi random graph with $N$ vertices of average degree $Z$, inserting a real symmetric $d \times d$ random block at each non-vanishing…

We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large central charge. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic…

Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…

We establish a large deviation principle for the empirical spectral measure of a sample covariance matrix with sub-Gaussian entries, which extends Bordenave and Caputo's result for Wigner matrices having the same type of entries [7]. To…

In this paper, we prove a universality result of convergence for a bivariate random process defined by the eigenvectors of a sample covariance matrix. Let $V_n=(v_{ij})_{i \leq n,\, j\leq m}$ be a $n\times m$ random matrix, where $(n/m)\to…

We introduce a generalized ensemble of nonhermitian matrices interpolating between the Gaussian Unitary Ensemble, the Ginibre ensemble and the Poisson ensemble. The joint eigenvalue distribution of this model is obtained by means of an…

We numerically analyze the spectral statistics of the multiparametric Gaussian ensembles of complex matrices with zero mean and variances with different decay routes away from the diagonals. As the latter mimics different degree of…

We discuss Bayesian inference for a known-mean Gaussian model with a compound symmetric variance-covariance matrix. Since the space of such matrices is a linear subspace of that of positive definite matrices, we utilize the methods of…

Let $\a$ be a real-valued random variable of mean zero and variance 1. Let $M_n(\a)$ denote the $n \times n$ random matrix whose entries are iid copies of $\a$ and $\sigma_n(M_n(\a))$ denote the least singular value of $M_n(\a)$.…

Random Hermitian matrices with a source term arise, for instance, in the study of non-intersecting Brownian walkers \cite{Adler:2009a, Daems:2007} and sample covariance matrices \cite{Baik:2005}. We consider the case when the $n\times n$…