Universality for Random Matrix Flows with Time-dependent Density
Probability
2015-04-16 v2 Mathematical Physics
math.MP
Abstract
We show that the Dyson Brownian Motion exhibits local universality after a very short time assuming that local rigidity and level repulsion hold. These conditions are verified, hence bulk spectral universality is proven, for a large class of Wigner-like matrices, including deformed Wigner ensembles and ensembles with non-stochastic variance matrices whose limiting densities differ from the Wigner semicircle law.
Cite
@article{arxiv.1504.00650,
title = {Universality for Random Matrix Flows with Time-dependent Density},
author = {Laszlo Erdos and Kevin Schnelli},
journal= {arXiv preprint arXiv:1504.00650},
year = {2015}
}