Jeanne Boursier

We investigate the decay of correlations for the circular long-range Riesz gas, a system of particles interacting pairwise through an inverse-power kernel. Our approach is based on the analysis of a partial differential equation, named Helffer-Sjöstrand equation. We will present various analytical tools to obtain decay estimates on solutions, leading to optimal correlation estimates. As a byproduct, we show that the microscopic process converges in the vague topology to a unique point process, which extends the Sine beta process, well-known in random matrix theory.