Bulk eigenvalue statistics for random regular graphs

• Roland Bauerschmidt ^[1] ; Jiaoyang Huang ^[2] ; Antti Knowles ^[3] ; Horng-Tzer Yau ^[2]
  1. [1] University of Cambridge

     University of Cambridge

     Cambridge District, Reino Unido

     
  2. [2] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
  3. [3] University of Géneve (Switzerland)

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 1, 2017, págs. 3626-3663
• Idioma: inglés
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  • 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.