100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

Jeanne Boursier

Decay of correlations for the circular Riesz gas
Tuesday, 10 January, 2023 - 14:30 to 15:30
Résumé : 


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.

Institution de l'orateur : 
ENS Lyon
Thème de recherche : 
Salle : 
logo uga logo cnrs