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November 2017 Bulk eigenvalue statistics for random regular graphs
Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles, Horng-Tzer Yau
Ann. Probab. 45(6A): 3626-3663 (November 2017). DOI: 10.1214/16-AOP1145

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.

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Roland Bauerschmidt. Jiaoyang Huang. Antti Knowles. Horng-Tzer Yau. "Bulk eigenvalue statistics for random regular graphs." Ann. Probab. 45 (6A) 3626 - 3663, November 2017. https://doi.org/10.1214/16-AOP1145

Information

Received: 1 June 2015; Revised: 1 August 2016; Published: November 2017
First available in Project Euclid: 27 November 2017

zbMATH: 1379.05098
MathSciNet: MR3729611
Digital Object Identifier: 10.1214/16-AOP1145

Subjects:
Primary: 05C50, 05C80, 15B52, 60B20

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 6A • November 2017
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