This is a study of the universality of spectral statistics for large random matrices. Considered
are symmetric, Hermitian, or quaternion self-dual random matrices with independent …

We consider N× N symmetric or hermitian random matrices with independent, identically
distributed entries where the probability distribution for each matrix element is given by a …

Random matrix theory has developed in the last few years, in connection with various fields
of mathematics and physics. These notes emphasize the relation with the problem of …

We show absence of energy levels repulsion for the eigenvalues of random Schrödinger
operators in the continuum. We prove that, in the localization region at the bottom of the …

It is a classical result of Wigner that for an hermitian matrix with independent entries on and
above the diagonal, the mean empirical eigenvalue distribution converges weakly to the …

In a series of works published in the 1990-s, Kerov put forth various applications of the circle
of ideas centred at the Markov moment problem to the limiting shape of random continual …

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

It is known (Hofmann-Credner and Stolz (2008)[4]) that the convergence of the mean
empirical spectral distribution of a sample covariance matrix Wn= 1/nYnYnt to the Marčenko …

We investigate the spectral statistics of Hermitian matrices in which the elements are chosen
uniformly from $ U (1) $, called the uni-modular ensemble (UME), in the limit of large matrix …

We investigate the linear statistics of random matrices with purely imaginary Bernoulli
entries of the form H_pq=H_qp=±i, that are either independently distributed or exhibit global …