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
DOI: 10.1214/16-AOP1145
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Resumen
- 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.