Poisson statistics for beta ensembles on the real line at high temperature

Abstract

This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where $\beta N\to const\in (0,\infty )$, with $N$ the system size and $\beta$ the inverse temperature. In this regime, the convergence to the equilibrium measure is a consequence of a recent result on large deviation principle by Liu and Wu (Stochastic Processes and their Applications (2019)). 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.

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Cited by in corpus (6)

• Beta Jacobi ensembles and associated Jacobi polynomials
• On the mean Density of States of some matrices related to the beta ensembles and an application to the Toda lattice
• Large Deviations for Ablowitz-Ladik lattice, and the Schur flow
• Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, Circular $\beta$-ensemble and double confluent Heun equation
• Limit theorems for moment processes of beta Dyson's Brownian motions and beta Laguerre processes
• CLT for real beta-ensembles at high temperature