Gaultier Lambert: Stein's method for normal approximation of linear statistics of beta-ensembles

Stein's method for normal approximation of linear statistics of beta-ensembles
Abstract: In the first part, I will review the basic ideas of Stein’s method for normal approximation and present a new application which is valid for statistics which are approximate eigenfunctions of the infinitesimal generator of a Markov process. In the second part, I will report on some applications to random matrix theory. We will prove a CLT for polynomial linear statistics of the Gaussian Unitary Ensemble and discuss the generalizations to one-cut regular beta-ensembles and general linear statistics.
This is joint work with Michel Ledoux and Christian Webb, available at https://arxiv.org/abs/1706.10251.