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 $$\beta N \rightarrow const \in (0, \infty )$$, with N the system size and $$\beta $$ 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.