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arXiv:1504.00396math.PR

Random matrices: tail bounds for gaps between eigenvalues

Hoi Nguyen, Terence Tao, Van Vu

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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.

arXiv comments
Several typos corrected, new references and a new application added (40 pages)
Journal reference
DOI
Subjects
math.PRProbability math.COCombinatorics

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  1. Mathematician Measures the Repulsive Force Within Polynomials 1 comment

    • Not to shit on all of your middlebrow dismissals but mathematicians are known to steal language from other fields as metaphors for mathematical phenomena. Sometimes these metaphors are very rigorous and precise and sometimes they're fast and loose. Here, look, I found all these…

      danharajView on HNParent context

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