We focus on first order interacting particle systems, which can be viewed as over-damped Langevin equations. In the first part, we will look at the so-called random batch methods (RBM) for simulating the interacting particle systems. The algorithms are motivated by the mini-batch idea in machine learning. For some special cases, we show the convergence of RBMs for the first marginal under Wasserstein distance. In the second part, we look at the Coulomb interaction in 3D space. We show that as the number of particles go to infinity, almost surely, the empirical measure converges in law to weak solutions of the limiting nonlinear Fokker-Planck equation. This talk is based on joint works with Shi Jin (Shanghai Jiao Tong), Jian-Guo Liu (Duke University) and Pu Yu (Peking University).
Dr. Lei Li is currently a tenure-track faculty at Shanghai Jiao Tong University. Dr. Li obtained B.S. at Tsinghua Unviersity in 2010, and Ph.D. at University of Wisconsin-Madison in 2015. He worked as a Postdoc at Duke University before he joined SJTU in 2018.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai