β-ensembles at intermediary temperature

Abstract: In this talk, I’ll present the real β-ensembles of dimension N in the regime 1/N<<β(N)<<1. In this regime, the system is still described macroscopically by the usual semi-circle type equilibrium measure. However, at mesoscopic scales, a transition occurs: below a certain scale the correlations are not strong enough anymore and the system enters a Poissonian regime. In this talk, I will present a mesoscopic CLT for linear statistics illustrating this transition and the convergence of local statistics to those of a Poisson point process. This is based on joint works with my co-authors Gaultier Lambert, Michel Pain and Luke Peilen and the recent preprint arxiv:2609.25301.

MathematicsPhysics

Audience: researchers in the topic

Probability, Statistical Mechanics and Quantum Fields