Gaussian Beta Ensembles at High Temperature: Eigenvalue Fluctuations and Bulk Statistics

Fumihiko Nakano, Khanh Duy Trinh

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3 Citations (Scopus)


We study the limiting behavior of Gaussian beta ensembles in the regime where βn= const as n→ ∞. The results are (1) Gaussian fluctuations for linear statistics of the eigenvalues, and (2) Poisson convergence of the bulk statistics. (2) is an alternative proof of the result by Benaych-Georges and Péché (J Stat Phys 161(3):633–656, 2015) with the explicit form of the intensity measure.

Original languageEnglish
Pages (from-to)295-321
Number of pages27
JournalJournal of Statistical Physics
Issue number2
Publication statusPublished - Oct 1 2018


All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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