We investigate several important issues regarding the Random Batch Method (RBM) for second order interacting particle systems. We first show the uniform-in-time strong convergence for second order systems under suitable contraction conditions. Secondly, we propose the application of RBM for singular interaction kernels via kernel splitting strategy, and investigate numerically the application to molecular dynamics.

翻译：我们调查了有关第二顺序相交粒子系统随机批量法(RBM)的几个重要问题。 我们首先展示了在适当的收缩条件下二顺序系统在时间上的统一强烈趋同。 其次,我们提议通过内核分裂战略对单一互动内核应用成果管理制,并对分子动态的应用进行量化调查。