Related papers: Wigner random matrices with non-symmetrically dist…

We show that the spectral radius of an $N\times N$ random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from below by $ 2 \*\sigma - o(N^{-6/11+\epsilon}), $ where $\sigma^2 $ is the…

The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…

Let $A$ be a square random matrix of size $n$, with mean zero, independent but not identically distributed entries, with variance profile $S$. When entries are i.i.d. with unit variance, the spectral radius of $n^{-1/2}A$ converges to $1$…

We consider random $n\times n$ matrices $X$ with independent and centered entries and a general variance profile. We show that the spectral radius of $X$ converges with very high probability to the square root of the spectral radius of the…

We investigate the spectral norms of symmetric $N \times N$ matrices from two pseudo-random ensembles. The first is the pseudo-Wigner ensemble introduced in "Pseudo-Wigner Matrices" by Soloveychik, Xiang and Tarokh and the second is its…

In this article we show the existence of limiting spectral distribution of a symmetric random matrix whose entries come from a stationary Gaussian process with covariances satisfying a summability condition. We provide an explicit…

This paper extends a previous bound of order $O(n^{-1})$ of the authors (arXiv:1405.7820[math.PR]), for the rate of convergence in Kolmogorov distance of the expected spectral distribution of a Wigner random matrix ensemble to the…

We give an effective bound of the joint spectral radius $\rho(\Sigma)$ for a finite set $\Sigma$ of nonnegative matrices: For every $n$, \[ \sqrt[n]{\left(\frac{V}{UD}\right)^{D} \max_C \max_{i,j\in C} \max_{A_1,\dots,A_n\in\Sigma}(A_1\dots…

We introduce a new technique to prove bounds for the spectral radius of a random matrix, based on using Jensen's formula to establish the zerofreeness of the associated characteristic polynomial in a region of the complex plane. Our…

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…

The primary aim of this paper is to establish bounds on the joint spectral radius for a finite set of nonnegative matrices based on their diagonal elements. The efficacy of this approach is evaluated in comparison to existing and related…

We consider an ensemble of nxn real symmetric random matrices A whose entries are determined by independent identically distributed random variables that have symmetric probability distribution. Assuming that the moment 12+2delta of these…

We consider a dilute version of the Wigner ensemble of n-dimensional random matrices H such that each row has in average \rho_n non-zero elements. We study asymptotic properties of the spectral norm of H on the scale n^{-2/3} in the limit…

In this paper we consider Wigner random matrices -- symmetric n by n random matrices whose entries are independent identically distributed real random variables. We prove that the probability distribution of one or several eigenvalues close…

We obtain nonasymptotic bounds on the spectral norm of random matrices with independent entries that improve significantly on earlier results. If $X$ is the $n\times n$ symmetric matrix with $X_{ij}\sim N(0,b_{ij}^2)$, we show that…

Consider a square matrix with independent and identically distributed entries of zero mean and unit variance. It is well known that if the entries have a finite fourth moment, then, in high dimension, with high probability, the spectral…

In the present paper, we prove that under the assumption of the finite sixth moment for elements of a Wigner matrix, the convergence rate of its empirical spectral distribution to the Wigner semicircular law in probability is $O(n^{-1/2})$…

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…

We study the spectral properties of a class of random matrices of the form $S_n^{-} = n^{-1}(X_1 X_2^* - X_2 X_1^*)$ where $X_k = \Sigma^{1/2}Z_k$, for $k=1,2$, $Z_k$'s are independent $p\times n$ complex-valued random matrices, and…

In this paper we study ensembles of random symmetric matrices $\X_n = {X_{ij}}_{i,j = 1}^n$ with dependent entries such that $\E X_{ij} = 0$, $\E X_{ij}^2 = \sigma_{ij}^2$, where $\sigma_{ij}$ may be different numbers. Assuming that the…