Bulk eigenvalue statistics for random regular graphs

Roland Bauerschmidt; Jiaoyang Huang; Antti Knowles; Horng Tzer Yau

doi:10.1214/16-AOP1145

Bulk eigenvalue statistics for random regular graphs

Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles, Horng Tzer Yau

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the uniform random d-regular graph on N vertices, with d ∈ [N^α,N^2/3-α] for arbitrary α > 0. We prove that in the bulk of the spectrum the local eigenvalue correlation functions and the distribution of the gaps between consecutive eigenvalues coincide with those of the Gaussian orthogonal ensemble.

Original language	English (US)
Pages (from-to)	3626-3663
Number of pages	38
Journal	Annals of Probability
Volume	45
Issue number	6
DOIs	https://doi.org/10.1214/16-AOP1145
State	Published - Nov 1 2017

Keywords

Dyson Brownian motion
GOE
Random regular graphs
Spectral statistics
Switchings
Universality

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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abstract = "We consider the uniform random d-regular graph on N vertices, with d ∈ [Nα,N2/3-α] for arbitrary α > 0. We prove that in the bulk of the spectrum the local eigenvalue correlation functions and the distribution of the gaps between consecutive eigenvalues coincide with those of the Gaussian orthogonal ensemble.",

keywords = "Dyson Brownian motion, GOE, Random regular graphs, Spectral statistics, Switchings, Universality",

author = "Roland Bauerschmidt and Jiaoyang Huang and Antti Knowles and Yau, {Horng Tzer}",

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AU - Knowles, Antti

AU - Yau, Horng Tzer

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N2 - We consider the uniform random d-regular graph on N vertices, with d ∈ [Nα,N2/3-α] for arbitrary α > 0. We prove that in the bulk of the spectrum the local eigenvalue correlation functions and the distribution of the gaps between consecutive eigenvalues coincide with those of the Gaussian orthogonal ensemble.

AB - We consider the uniform random d-regular graph on N vertices, with d ∈ [Nα,N2/3-α] for arbitrary α > 0. We prove that in the bulk of the spectrum the local eigenvalue correlation functions and the distribution of the gaps between consecutive eigenvalues coincide with those of the Gaussian orthogonal ensemble.

KW - Dyson Brownian motion

KW - GOE

KW - Random regular graphs

KW - Spectral statistics

KW - Switchings

KW - Universality

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JF - Annals of Probability

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ER -

Bulk eigenvalue statistics for random regular graphs

Abstract

Keywords

ASJC Scopus subject areas

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