Convergence in total variation for the kinetic Langevin algorithm

We prove non-asymptotic total variation estimates for the kinetic Langevin algorithm in high dimension when the target measure satisfies a Poincaré inequality and has gradient Lipschitz potential. The main point is that the estimate improves significantly upon the corresponding bound for the non-kinetic version of the algorithm, due to Dalalyan. In particular, the dimension dependence drops from O(n) to O(\sqrt{n}) .