Invited speakers & discussants

Bio: Arnaud Guilin is Professor at Université Clermont Auvergne, and Deputy Director at CNRS Mathematics, director of the Program Maths-Vives. His themes of research are probability and its interactions with PDE: convergence to equilibrium, mean field particle systems...

Title: Convergence to equilibrium of some non reversible process via Lift/Collapse and Flow Poincaré inequality

Abstract: Convergence to equilibrium of the underdamped Langevin process or of some piecewise deterministic sampler has attracted many interesting methodologies starting from the works of Herau and then Villani on hypocercivity and of Dolbeault-Mouhaut-Schmeiser. If quantitative rates can be achieved, they often are not of the correct order being of the order of the spectral gap of the invariant measures. Recently Albritton-Armstrong-Mourrat-Novack have derived a variational approach which has enabled Cao-Lu-Wang or Lu-Wang to obtain correct order wrt the spectral gap or dimension dependance. By using the concept of lift/collapse processes, we present here a general methodology which allows for quite diverse collapse process (overdamped Langevin process, sticky Brownian motion, ...) and prove convergence to equilibrium, via a novel Flow Poincaré inequality, of underdamped Langevin process, PDMP sampler or jamming particles.
(In collaboration with Andreas Eberle, Leo Hahn, Francis Loerler, Manon Michel)