Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations
Guillin, Arnaud; Gentil, Ivan; Bolley, François (2012), Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations, Journal of Functional Analysis, 263, 8, p. 2430-2457. http://dx.doi.org/10.1016/j.jfa.2012.07.007
Type
Article accepté pour publication ou publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00632941/fr/Date
2012Journal name
Journal of Functional AnalysisVolume
263Number
8Publisher
Elsevier
Pages
2430-2457
Publication identifier
Metadata
Show full item recordAbstract (EN)
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.Subjects / Keywords
spectral gap; functional inequalities; Wasserstein distance; Diffusion equationsRelated items
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