Fixed energy universality for generalized Wigner matrices
Probability
2015-04-17 v3 Mathematical Physics
math.MP
Abstract
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 the energy parameter or they hold only for Hermitian matrices if the energy parameter is fixed. We develop a homogenization theory of the Dyson Brownian motion and show that microscopic universality follows from mesoscopic statistics.
Cite
@article{arxiv.1407.5606,
title = {Fixed energy universality for generalized Wigner matrices},
author = {Paul Bourgade and Laszlo Erdos and Hong-Tzer Yau and Jun Yin},
journal= {arXiv preprint arXiv:1407.5606},
year = {2015}
}