We study contraction for the kinetic Fokker-Planck operator on the torus. Solving the stochastic differential equation, we show contraction and therefore exponential convergence in the Monge-Kantorovich-Wasserstein $ \mathcal{W}_2$ 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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