Central limit theorem and local laws for beta-ensembles

par Michel Pain (CNRS & Université Toulouse III)

jeudi 23 oct. 2025, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (ICJ)

A beta-ensembles is a system of $N$ particles on the real line confined by a potential $V$ and interacting via logarithmic repulsion. I will explain the usual approach to prove central limit theorems for linear statistics and the method we introduced with Paul Bourgade and Krishnan Mody to prove local laws when $V$ is analytic. Finally, I will present a recent paper with Charlie Dworaczek Guera and Ronan Memin where we combine them to prove a central limit theorem in the case of the singular potential $V(x)=|x|^p$ for $p>2$.