Convergence to equilibrium for linear Fokker-Planck equations

Abstract

In this note, we investigate the spectral analysis and long time asymptotic convergence of semigroups associated to discrete, fractional and classical Fokker-Planck equations in some regime where the corresponding operators are close. We successively deal with the discrete and the classical Fokker-Planck model and the fractional and the classical Fokker-Planck model. In each case, we present results of uniform convergence to equilibrium based on perturbation and/or enlargement arguments and obtained in collaboration with S. Mischler in [7].