Related papers: Wigner theorems for random matrices with dependent…

We prove that the local eigenvalue statistics of real symmetric Wigner-type matrices near the cusp points of the eigenvalue density are universal. Together with the companion paper [arXiv:1809.03971], which proves the same result for the…

We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and stochastically independent diagonals. Along the diagonals the entries may be…

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…

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…

This paper considers the problem of testing for latent structure in large symmetric data matrices. The goal here is to develop statistically principled methodology that is flexible in its applicability, computationally efficient, and…

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…

We consider the non-Hermitian analogue of the celebrated Wigner-Dyson-Mehta bulk universality phenomenon, i.e. that in the bulk the local eigenvalue statistics of a large random matrix with independent, identically distributed centred…

We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral Random Matrix Theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in…

We extend the random characteristics approach to Wigner matrices whose entries are not required to have a normal distribution. As an application, we give a simple and fully dynamical proof of the weak local semicircle law in the bulk.

In this paper we consider a new normalization of matrices obtained by choosing distinct codewords at random from linear codes over finite fields and find that under some natural algebraic conditions of the codes their empirical spectral…

This paper proves universality of the distribution of the smallest and largest gaps between eigenvalues of generalized Wigner matrices, under some smoothness assumption for the density of the entries. The proof relies on the Erd{\H…

For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local…

We characterize the limiting second order distributions of certain independent complex Wigner and deterministic matrices using Voiculescu's notions of freeness over the diagonal. If the Wigner matrices are Gaussian, Mingo and Speicher's…

Since E.P.Wigner (1958) established his famous semicircle law, lots of attention has been paid by physicists, probabilists and statisticians to study the asymptotic properties of the largest eigenvalues for random matrices. Bai and Yin…

We prove the Wigner-Dyson-Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random matrices either require an averaging in…

We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift $\binom{j}{2} \omega+jy+x \mod 1$ for irrational $\omega$. We prove that the eigenvalue distribution of…

This paper is a continuation of our paper "Fluctuations of Matrix Elements of Regular Functions of Gaussian Random Matrices", J. Stat. Phys. (134), 147--159 (2009), in which we proved the Central Limit Theorem for the matrix elements of…

We prove the Central Limit Theorem for finite-dimensional vectors of linear eigenvalue statistics of submatrices of Wigner random matrices under the assumption that test functions are sufficiently smooth. We connect the asymptotic…

In this article, we consider random Wigner matrices, that is symmetric matrices such that the subdiagonal entries of Xn are independent, centered, and with variance one except on the diagonal where the entries have variance two. We prove…

We prove universality at the edge for rescaled correlation functions of Wigner random matrices in the limit $n\to +\infty$. As a corollary, we show that, after proper rescaling, the 1st, 2nd, 3rd, etc. eigenvalues of Wigner random hermitian…