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arXiv · 1505.06700

Bulk eigenvalue statistics for random regular graphs

Roland Bauerschmidt·Jiaoyang Huang·Antti Knowles·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.

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Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles, Horng-Tzer Yau. 2015-05-25. Bulk eigenvalue statistics for random regular graphs. https://doi.org/10.1214/16-aop1145

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