On the Random Batch Method for Second Order Interacting Particle Systems

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 of RBM for second order systems under suitable contraction conditions when the interaction kernels are regular. Second, we propose some variants of RBM for second order systems that can have singular interaction kernels via a kernel splitting strategy, and investigate numerically the application of such methods to molecular dynamics.