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

Fumihiko Nakano, Khanh Duy Trinh

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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
Volume173
Issue number2
DOIs
Publication statusPublished - 2018 Oct 1
Externally publishedYes

Keywords

  • Bulk statistics
  • Gaussian beta ensembles
  • Global fluctuations
  • High temperature
  • Poisson statistics
  • Random Jacobi matrices

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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