Mathieu Lewin -- Mini-course: Riesz and Coulomb gases: what's known and unknown
Channel: Matrices Et Graphes Aléatoires GDR CNRS
Date: 2021-04-30

Abstract: In this lecture I will speak about a family of random point processes of Gibbs type, on the whole d-dimensional space, which includes many examples from random matrix theory (such as GUE, GOE and Ginibre). The points are assumed to interact by pairs through the Riesz/Coulomb potentials, and a parameter playing the role of a temperature is used to adjust the amount of randomness. I will try to review what is expected on physical ground for these processes and what has been rigorously established so far. The talk will thus be focused on open problems.