Convergence to equilibrium for the kinetic Fokker-Planck equation on the torus
Abstract
We study convergence to equilibrium for the kinetic Fokker-Planck equation on the torus. Solving the stochastic differential equation, we show exponential convergence in the Monge-Kantorovich-Wasserstein W2 distance. Finally, we investigate if such a coupling can be obtained by a co-adapted coupling, and show that then the bound must depend on the square root of the initial distance.
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