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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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

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

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

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Zentralblatt MATH identifier

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

Random regular graphs spectral statistics universality GOE switchings Dyson Brownian motion


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.

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