Asymptotic properties of the density of particles in $\beta$-ensembles

TL;DR

This paper investigates the long-term behavior of particle densities in beta-ensembles, establishing large deviation principles and mod-Gaussian convergence for various potentials as the number of particles grows large.

Contribution

It extends the asymptotic analysis of particle densities in beta-ensembles by proving large deviation principles and mod-Gaussian convergence for general potentials.

Findings

Large deviation principle for log-density in beta-ensembles.

Mod-Gaussian convergence in classical examples.

Asymptotic properties as the number of particles tends to infinity.

Abstract

We extend recent results on the Asymptotic Equipartition Property for the density of $n$ particles in $\beta$-ensembles, as $n$ tends to infinity. We prove the Large Deviation Principle of the log-density for a general potential and the mod-gaussian convergence in the classical examples.