Entropy and the Shannon-McMillan-Breiman theorem for 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.

We made small changes suggested by the referees. In particular, we updated the bibliography

References in corpus (2)

• Fluctuations of linear eigenvalue statistics of $\beta$ matrix models in the multi-cut regime
• Matrix models for circular ensembles

Cited by in corpus (1)

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