Entropy and the Shannon-McMillan-Breiman theorem for beta random matrix ensembles

TL;DR

This paper establishes the asymptotic equipartition property and a Central Limit Theorem for eigenvalue densities in beta random matrix ensembles with real analytic potentials, advancing understanding of their statistical behavior.

Contribution

It introduces the asymptotic equipartition property and a CLT for eigenvalue densities in beta ensembles with real analytic potentials, which were not previously established.

Findings

Proved asymptotic equipartition property for beta ensembles.

Established a Central Limit Theorem for eigenvalue densities.

Enhanced understanding of statistical properties of beta random matrix ensembles.

Abstract

We show that beta ensembles in Random Matrix Theory with generic real analytic potential have the asymptotic equipartition property. In addition, we prove a Central Limit Theorem for the density of the eigenvalues of these ensembles.