  We study the kinetic Fokker-Planck equation on the whole space with a
confining potential. We show quantitative rates of exponential convergence to
equilibrium in a well chosen Wasserstein-1 distance. We use the Wasserstein-1
version of Harris's theorem introduced by Hairer and Mattingly. We make use of
similarities between hypocoercivity and hypoellipticity in order to use
Malliavin calculus to see hypocoercivity for this equation on the level of the
SDE.
