The Annals of Probability

Bulk eigenvalue statistics for random regular graphs

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

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Abstract

We consider the uniform random $d$-regular graph on $N$ vertices, with $d\in[N^{\alpha},N^{2/3-\alpha}]$ for arbitrary $\alpha>0$. 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.

Article information

Source
Ann. Probab., Volume 45, Number 6A (2017), 3626-3663.

Dates
Received: June 2015
Revised: August 2016
First available in Project Euclid: 27 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.aop/1511773660

Digital Object Identifier
doi:10.1214/16-AOP1145

Mathematical Reviews number (MathSciNet)
MR3729611

Zentralblatt MATH identifier
1379.05098

Subjects
Primary: 05C80: Random graphs [See also 60B20] 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.) 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 15B52: Random matrices

Keywords
Random regular graphs spectral statistics universality GOE switchings Dyson Brownian motion

Citation

Bauerschmidt, Roland; Huang, Jiaoyang; Knowles, Antti; Yau, Horng-Tzer. Bulk eigenvalue statistics for random regular graphs. Ann. Probab. 45 (2017), no. 6A, 3626--3663. doi:10.1214/16-AOP1145. https://projecteuclid.org/euclid.aop/1511773660


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