Local eigenvalue statistics for random matrices with general short range correlations

Oskari Ajanki, Laszlo Erdos, Torben Krüger

Published 2016-04-27Version 1

We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the Green function and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but otherwise are of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation that gives the deterministic limit of the Green function.