Exponential decay of Rényi divergence under Fokker-Planck equations

Abstract

We prove the exponential convergence to the equilibrium, quantified by Rényi divergence, of the solution of the Fokker-Planck equation with drift given by the gradient of a strictly convex potential. This extends the classical exponential decay result on the relative entropy for the same equation.

Exponential convergence rate in Theorem 1.2 has been improved and a simpler proof is provided