Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

  title={Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations},
  author={François Bolley and Ivan Gentil and Arnaud Guillin},
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… CONTINUE READING

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Uniform convergence to equilibrium for granular media

  • F. Bolley, I. Gentil, A. Guillin
  • 2012

Reflection coupling and Wasserstein contractivity without convexity

  • A. Eberle
  • 2011

Optimal transport, Old and new, volume

  • C. Villani
  • 2009

A simple proof of the Poincaré inequality for a large class of probability measures including the log-concave case

  • D. Bakry, F. Barthe, P. Cattiaux, A. Guillin
  • Elec. Comm. Prob.,
  • 2008

Gradient flows in metric spaces and in the space of probability measures

  • L. Ambrosio, N. Gigli, G. Savaré
  • Lectures in Math. ETH Zürich. Birkhäuser, Basel…
  • 2008

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