Mean field limit for large systems of particles
Student No.:40
Time:Fri 10:30-11:50 & 13:30-15:05, Jan.11
Instructor:王振富 Wang Zhenfu (University of Pennsylvania)  
Place:10:30-11:50 at Lecture Hall, 13:30-15:05 at Conference Room 3, Jin Chun Yuan West Bldg.
Starting Date:2019-1-11
Ending Date:2019-1-11

Large systems of interacting particles are now ubiquitous. The corresponding microscopic models are usually conceptually simple, based for instance on Newton's 2nd law. However they are analytically and computationally complicated since the number $N$ of particles is very large. Understanding how this complexity can be reduced is a challenging but critical question with potentially deep impact in various fields and a wide range of applications: in physics where particles can represent ions and electrons in plasma, or molecules in a fluid and even galaxies in some cosmological models; in the bio-sciences where they typically model micro-organisms (cells or bacteria); in economics or social sciences where particles are individual agents. In these talks, we focus on the mean field limit and/or propagation of chaos for large systems of particles with singular interacting forces. We introduced the relative entropy method to quantify the propagation of chaos for large stochastic or deterministic systems of interacting particles. This approach requires to prove large deviations estimates for non-continuous potentials modified by the limiting law. But it leads to explicit convergence rates for all marginals. Recent successes include the Vlasov systems with bounded interaction forces and 2D Navier-Stokes and 2D Euler. We will discuss some recent progresses and some open problems if time permitted.