Poisson Statistics for Beta Ensembles on the Real Line at High Temperature

Fumihiko Nakano, Khanh Duy Trinh

Research output: Contribution to journalArticle

Abstract

This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where βN→ const∈ (0 , ∞) , with N the system size and β the inverse temperature. For the global behavior, the convergence to the equilibrium measure is a consequence of a recent result on large deviation principle. This paper focuses on the local behavior and shows that the local statistics around any fixed reference energy converges weakly to a homogeneous Poisson point process.

Original languageEnglish
Pages (from-to)632-649
Number of pages18
JournalJournal of Statistical Physics
Volume179
Issue number2
DOIs
Publication statusPublished - 2020 Apr 1

Keywords

  • Beta ensembles
  • High temperature
  • Large deviation principle
  • Poisson statistics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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