Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics

Abstract

We study the limiting behavior of Gaussian beta ensembles in the regime where $\beta n=const$ as $n\to \infty$. The results are (1) Gaussian fluctuations for linear statistics of the eigenvalues, and (2) Poisson convergence of the bulk statistics. (2) is an alternative proof of the result by F.~Benaych-Georges and S.~Péché (2015) with the explicit form of the intensity measure.

We corrected the proof of the local law

References in corpus (3)

• Continuum limits of random matrices and the Brownian carousel
• Eigenvector localization for random band matrices with power law band width
• From Sine kernel to Poisson statistics