Bulk eigenvalue statistics for random regular graphs

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

Published 2015-05-25Version 1

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.