Mini-course: Riesz and Coulomb gases: what's known and unknown.

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.

statistical mechanicsmathematical physicsprobability

Audience: advanced learners

Séminaire MEGA

Series comments: Description: Monthly seminar on random matrices and random graphs