Related papers: The semicircle law for matrices with independent d…
We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…
We study the empirical spectral distribution (ESD) of symmetric random matrices with ergodic entries on the diagonals. We observe that for entries with correlations that decay to 0, when the distance of the diagonal entries becomes large…
We consider the empirical eigenvalue distribution of random real symmetric matrices with stochastically independent skew-diagonals and study its limit if the matrix size tends to infinity. We allow correlations between entries on the same…
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…
We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic…
In this paper, we derive limit laws for the empirical spectral distributions of random band and block matrices with correlated entries. In the first part of the paper, we study band matrices with approximately uncorrelated entries. We…
We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of…
We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on the…
This paper studies the spectral behavior of large dimensional Chatterjee's rank correlation matrix when observations are independent draws from a high-dimensional random vector with independent continuous components. We show that the…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
We study ensembles of random symmetric matrices whose entries exhibit certain correlations. Examples are distributions of Curie-Weiss-type. We provide a criterion on the correlations ensuring the validity of Wigner's semicircle law for the…
In this note, we show that the limiting spectral distribution of symmetric random matrices with stationary entries is absolutely continuous under some sufficient conditions. This result is applied to obtain sufficient conditions on a…
For two lacunary sequences $(M_{n,1})_{n\geq 2},(M_{n,2})_{n\geq 0}$ and suitable functions $f$ we introduce random matrix ensembles with \begin{equation*} X_{n,n'}=f(M_{n+n',1}x_1,M_{|n-n'|,2}x_2). \end{equation*} We prove weak convergence…
We consider random hermitian matrices in which distant above-diagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of eigenvalues by combinatorial methods. We also prove that…
We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent real entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on…
In this paper we consider ensemble of random matrices $\X_n$ with independent identically distributed vectors $(X_{ij}, X_{ji})_{i \neq j}$ of entries. Under assumption of finite fourth moment of matrix entries it is proved that empirical…
We explore the validity of the circular law for random matrices with non i.i.d. entries. Let A be a random n \times n real matrix having as a random vector in R^{n^2} a log-concave isotropic unconditional law. In particular, the entries are…
For symmetric random matrices with correlated entries, which are functions of independent random variables, we show that the asymptotic behavior of the empirical eigenvalue distribution can be obtained by analyzing a Gaussian matrix with…
We analyze the empirical spectral distribution of random periodic band matrices with correlated entries. The correlation structure we study was first introduced in 2015 by Hochst\"attler, Kirsch and Warzel, who named their setup "almost…
We consider random Hermitian matrices with independent upper triangular entries. Wigner's semicircle law says that under certain additional assumptions, the empirical spectral distribution converges to the semicircle distribution. We…