Exponential decay of R\'enyi divergence under Fokker-Planck equations

TL;DR

This paper proves that solutions to the Fokker-Planck equation with convex potential drift converge exponentially to equilibrium when measured by Re9nyi divergence, extending classical entropy decay results.

Contribution

It extends classical exponential decay results from relative entropy to Re9nyi divergence for Fokker-Planck equations with convex potentials.

Findings

Exponential convergence to equilibrium in Re9nyi divergence.

Extension of entropy decay results to Re9nyi divergence.

Applicable to Fokker-Planck equations with strictly convex potentials.

Abstract

We prove the exponential convergence to the equilibrium, quantified by R\'enyi 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.