J. Bauerschmidt, Roland",iaoyang," Knowles",antti," Yau",horng-tzer,"huang,, Bulk eigenvalue statistics for random regular graphs, Annals of probability (Online) , 45(6A), 2017, pp. 3626-3663
We consider the uniform random d-regular graph on N vertices, with d.[N.,N2/3..] for arbitrary .>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.