Skip to Main content Skip to Navigation
Journal articles

Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

Abstract : We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional inequality, which links the distance with its dissipation and ensures a spectral gap in Wasserstein distance. We give practical criteria for this inequality and compare it to classical ones. The key point is to quantify the contribution of the diffusion term to the rate of convergence, which to our knowledge is a novelty.
Document type :
Journal articles
Complete list of metadatas

Cited literature [28 references]  Display  Hide  Download
Contributor : Ivan Gentil <>
Submitted on : Tuesday, September 18, 2012 - 4:42:40 PM
Last modification on : Wednesday, September 23, 2020 - 4:28:22 AM
Long-term archiving on: : Wednesday, December 19, 2012 - 3:45:01 AM


Files produced by the author(s)



François Bolley, Ivan Gentil, Arnaud Guillin. Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations. Journal of Functional Analysis, Elsevier, 2012, 263 (8), pp.2430-2457. ⟨10.1016/j.bbr.2011.03.031⟩. ⟨hal-00632941v2⟩



Record views


Files downloads