We provide a framework to prove convergence rates for discretizations of kinetic Langevin dynamics for $M$-$\nabla$Lipschitz $m$-log-concave densities. Our approach provides convergence rates of $\mathcal{O}(m/M)$, with explicit stepsize restrictions, which are of the same order as the stability threshold for Gaussian targets and are valid for a large interval of the friction parameter. We apply this methodology to various integration methods which are popular in the molecular dynamics and machine learning communities. Finally we introduce the property ``$\gamma$-limit convergent" (GLC) to characterise underdamped Langevin schemes that converge to overdamped dynamics in the high friction limit and which have stepsize restrictions that are independent of the friction parameter; we show that this property is not generic by exhibiting methods from both the class and its complement.

翻译：我们提供了一个框架来证明以美元-纳布拉$Lipschitz 美元- log- concave 密度为美元- log- concave 密度的动态朗埃文动态分解的趋同率。 我们的方法提供了明确的分级限制,这与高山目标的稳定阈值相同,并且对摩擦参数的较大间隔有效。 我们对分子动态和机器学习社区中流行的各种集成方法采用了这种方法。 最后,我们引入了“$\gamma$- limit commont” (GLC) 属性, 来描述高摩擦限度中被压得过大的朗埃文计划(GLC), 其特征为高摩擦限度中被压得过大的动态, 并且使与摩擦参数不同的限制逐步化; 我们表明,这种属性不是通用的, 其方法是从阶级及其补充中展示出的方法。</s>