内容介绍：In the first part of the talk, we will have a brief introduction to Markov Chain Monte Carlo methods for sampling from a given distribution, especially those methods involving Stochastic Differential Equations (SDEs). In the second part, we focus on speeding sampling from the Gibbs distribution for many body systems. We will introduce both an MC and an MD algorithm that we propose recently, in which we use random batch ideas to speed up the computation. In the Random Batch Monte Carlo method, a singular potential is split into a smooth long range part and a singular short range part. The smooth part with random batch strategy is used to generate a proposal sample, and the singular part is used for a Metropolis rejection. This reduces the computational cost for sampling from O(N) to O(1) in one iteration. In the random batch Ewald method, we apply the random batch idea in frequency domain to obtain an efficient molecular dynamics method.