Stability of the Matrix Dyson Equation and Random Matrices with Correlations
Probability
2018-03-01 v5 Mathematical Physics
math.MP
Abstract
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.
Keywords
Cite
@article{arxiv.1604.08188,
title = {Stability of the Matrix Dyson Equation and Random Matrices with Correlations},
author = {Oskari Ajanki and Laszlo Erdos and Torben Krüger},
journal= {arXiv preprint arXiv:1604.08188},
year = {2018}
}
Comments
Format was adjusted to coincide with the published version in PTRF