Random matrices: tail bounds for gaps between eigenvalues
Probability
2015-05-05 v3 Combinatorics
Abstract
Gaps (or spacings) between consecutive eigenvalues are a central topic in random matrix theory. The goal of this paper is to study the tail distribution of these gaps in various random matrix models. We give the first repulsion bound for random matrices with discrete entries and the first super-polynomial bound on the probability that a random graph has simple spectrum, along with several applications.
Cite
@article{arxiv.1504.00396,
title = {Random matrices: tail bounds for gaps between eigenvalues},
author = {Hoi Nguyen and Terence Tao and Van Vu},
journal= {arXiv preprint arXiv:1504.00396},
year = {2015}
}
Comments
Several typos corrected, new references and a new application added (40 pages)