Edge Universality of Beta Ensembles

Paul Bourgade, László Erdös, Horng Tzer Yau

Research output: Contribution to journalArticlepeer-review


We prove the edge universality of the beta ensembles for any β ≥ 1, provided that the limiting spectrum is supported on a single interval, and the external potential is C4 and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class C4.

Original languageEnglish (US)
Pages (from-to)261-353
Number of pages93
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Nov 2014

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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