Exponential Decay of Rényi Divergence Under Fokker–Planck Equations

Yu Cao, Jianfeng Lu, Yulong Lu

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1172-1184
Number of pages13
JournalJournal of Statistical Physics
Issue number5
StatePublished - Sep 1 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.


  • Exponential convergence
  • Fokker–Planck equation
  • Gradient flow
  • Rényi divergence


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