Resumen de Bulk eigenvalue statistics for random regular graphs

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

• We consider the uniform random dd-regular graph on NN vertices, with d∈[Nα,N2/3−α]d∈[Nα,N2/3−α] for arbitrary α>0α>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.