We prove non asymptotic total variation estimates for the kinetic Langevin algorithm in high dimension when the target measure satisfies a Poincar\'e 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 $O(\sqrt n)$.

翻译：当目标测度满足庞加莱不等式且具有梯度利普希茨势时，我们证明了高维情形下动力学朗之万算法的非渐近全变差估计。核心结论在于：相较于Dalalyan提出的非动力学版本算法的对应边界，该估计值有显著改进。具体而言，维度依赖项从$O(n)$降至$O(\sqrt n)$。