Random Matrices with Slow Correlation Decay
Probability
2020-06-01 v5 Mathematical Physics
math.MP
Abstract
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of [arXiv:1604.08188] to allow slow correlation decay and arbitrary expectation. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.
Cite
@article{arxiv.1705.10661,
title = {Random Matrices with Slow Correlation Decay},
author = {László Erdős and Torben Krüger and Dominik Schröder},
journal= {arXiv preprint arXiv:1705.10661},
year = {2020}
}
Comments
41 pages, 1 figure. We corrected a typo in (4.1b)