Bulk eigenvalue statistics for random regular graphs

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

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish (US)
Pages (from-to)3626-3663
Number of pages38
JournalAnnals of Probability
Issue number6
StatePublished - Nov 1 2017


  • Dyson Brownian motion
  • GOE
  • Random regular graphs
  • Spectral statistics
  • Switchings
  • Universality

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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