Jeanne Boursier (Columbia University)

Title: Statistical mechanics of the circular Riesz gas.

Abstract: I will present results on the statistical mechanics of the one-dimensional Riesz gas, a particle system with repulsive power-law interactions. This model extends the log-gas, well-known in random matrix theory. Through the study of a partial differential equation, sometimes called the Helffer-Sjöstrand equation, we establish optimal fluctuations and correlations estimates. I will then explain how to prove the existence of a unique infinite volume limit for the Riesz gas.