Related papers: Non-Hermitian random matrices with a variance prof…

For each $n$, let $A_n=(\sigma_{ij})$ be an $n\times n$ deterministic matrix and let $X_n=(X_{ij})$ be an $n\times n$ random matrix with i.i.d. centered entries of unit variance. We study the asymptotic behavior of the empirical spectral…

Consider a $N\times n$ random matrix $Y_n=(Y_{ij}^{n})$ where the entries are given by $Y_{ij}^{n}=\frac{\sigma(i/N,j/n)}{\sqrt{n}} X_{ij}^{n}$, the $X_{ij}^{n}$ being centered i.i.d. and $\sigma:[0,1]^2 \to (0,\infty)$ being a continuous…

We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure $\mu$ of large random real symmetric matrices with heavy tailed entries. Specifically, consider the N by N symmetric matrix $Y_N^\sigma$…

Consider the random matrix $\Sigma = D^{1/2} X \widetilde D^{1/2}$ where $D$ and $\widetilde D$ are deterministic Hermitian nonnegative matrices with respective dimensions $N \times N$ and $n \times n$, and where $X$ is a random matrix with…

Consider an $N\times n$ random matrix $Y_n=(Y^n_{ij})$ where the entries are given by $Y^n_{ij}=\frac{\sigma_{ij}(n)}{\sqrt{n}}X^n_{ij}$, the $X^n_{ij}$ being independent and identically distributed, centered with unit variance and…

We consider $n\times n$ non-Hermitian random matrices with independent entries and a variance profile, as well as an additive deterministic diagonal deformation. We show that their empirical eigenvalue distribution converges to a limiting…

Let $\mathbf{a}_{ij}$, $1\leq i\leq j\leq n$, be independent random variables and $\mathbf{a}_{ji}=\mathbf{a}_{ij}$, for all $i,j$. Suppose that every $\mathbf{a}_{ij}$ is bounded, has zero mean, and its variance is given by…

For fixed $m>1$, we consider $m$ independent $n \times n$ non-Hermitian random matrices $X_1, ..., X_m$ with i.i.d. centered entries with a finite $(2+\eta)$-th moment, $ \eta>0.$ As $n$ tends to infinity, we show that the empirical…

We investigate concentration properties of spectral measures of Hermitian random matrices with partially dependent entries. More precisely, let $X_n$ be a Hermitian random matrix of size $n\times n$ that can be split into independent blocks…

We consider a class of sparse random matrices of the form $A_n =(\xi_{i,j}\delta_{i,j})_{i,j=1}^n$, where $\{\xi_{i,j}\}$ are i.i.d.~centered random variables, and $\{\delta_{i,j}\}$ are i.i.d.~Bernoulli random variables taking value $1$…

Consider a $N\times n$ random matrix $Y_n=(Y_{ij}^{n})$ where the entries are given by $$ Y_{ij}^{n}=\frac{\sigma_{ij}(n)}{\sqrt{n}} X_{ij}^{n} $$ the $X_{ij}^{n}$ being centered, independent and identically distributed random variables…

We consider $n^2\times n^2$ real symmetric and hermitian matrices $M_n$, which are equal to sum of $m_n$ tensor products of vectors $X^\mu=B(Y^\mu\otimes Y^\mu)$, $\mu=1,\dots,m_n$, where $Y^\mu$ are i.i.d. random vectors from $\mathbb R^n…

It is a result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n\times n$ Gaussian matrix with independent entries of mean zero and unit variance are asymptotically given by the determinantal point process…

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 $M_n(\a)$.…

This paper is centred on the spectral study of a Random Fourier matrix, that is an $n\times n$ matrix $A$ whose $(j, k)$ entries are $\exp(2i\pi m X_jY_k)$, with $X_j$ and $Y_k$ two i.i.d sequences of random variables and $1\leq m\leq n$ is…

In this article, we study the fluctuations of the random variable: $$ {\mathcal I}_n(\rho) = \frac 1N \log\det(\Sigma_n \Sigma_n^* + \rho I_N),\quad (\rho>0) $$ where $\Sigma_n= n^{-1/2} D_n^{1/2} X_n\tilde D_n^{1/2} +A_n$, as the…

Consider $N\times N$ Hermitian or symmetric random matrices $H$ where the distribution of the $(i,j)$ matrix element is given by a probability measure $\nu_{ij}$ with a subexponential decay. Let $\sigma_{ij}^2$ be the variance for the…

We consider products of independent square random non-Hermitian matrices. More precisely, let $n\geq 2$ and let $X_1,\ldots,X_n$ be independent $N\times N$ random matrices with independent centered entries with variance $N^{-1}$. It was…

Let $\{x_{\alpha}\}_{\alpha \in \mathbb{Z}}$ and $\{y_{\alpha}\}_{\alpha \in \mathbb{Z}}$ be two independent collections of zero mean, unit variance random variables with uniformly bounded moments of all orders. Consider a nonsymmetric…

Let $A_n$ be an $n\times n$ random symmetric matrix with $(A_{ij})_{i< j}$ i.i.d. mean $0$, variance 1, following a subGaussian distribution and diagonal elements i.i.d. following a subGaussian distribution with a fixed variance. We…