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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.

Keywords

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)

R2 v1 2026-06-22T09:08:29.251Z