Ergodicity and long-time behavior of the Random Batch Method for interacting particle systems

We study the geometric ergodicity and long-time behavior of Random Batch Method for interacting particle systems, which exhibits superior numerical performance in recent large-scale scientific computing experiments. show that both system (IPS) random batch (RB–IPS), distribution laws converge to their respective invariant distributions exponentially, convergence rate does not depend on number particles [Formula: see text], time step text] divisions or size text]. Moreover, Wasserstein-1 distance between IPS RB–IPS is bounded by showing can be used sample accurately with greatly reduced computational cost.