Random matrices: tail bounds for gaps between eigenvalues

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-poly...

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Veröffentlicht in:	Probability theory and related fields 2017-04, Vol.167 (3-4), p.777-816
Hauptverfasser:	Nguyen, Hoi, Tao, Terence, Vu, Van
Format:	Artikel
Sprache:	eng
Schlagworte:	Economics Eigenvalues Finance Graphs Insurance Management Mathematical and Computational Biology Mathematical and Computational Physics Mathematics Mathematics and Statistics Matrix theory Operations Research/Decision Theory Probability Probability theory Probability Theory and Stochastic Processes Quantitative Finance Random variables Statistics for Business Studies Theoretical
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Zusammenfassung:	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.
ISSN:	0178-8051 1432-2064
DOI:	10.1007/s00440-016-0693-5