Abstract: 

We prove the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the Patlak-Keller-Segel model in optimal subcritical regimes is obtained for the first time. To give an answer to this longstanding problem, we take advantage of a new modulated free energy and we prove some precise large deviation estimates encoding the competition between diffusion and attraction. This modulated free energy approach can also treat the systems with a wide range of repulsive kernels, including the vanishing viscosity case. Based on joint works with D. Bresch and P.-E. Jabin.

个人简介：

王振富，2012年本科毕业于南京大学，2017年获美国马里兰大学数学博士学位，博士导师为 Pierre-Emmanuel Jabin。2017年7月到2020年6月在美国宾夕法尼亚大学从事博士后研究工作。2020年10月入职北京大学，现任北京国际数学研究中心助理教授、研究员。主要研究领域为交互粒子系统的平均场极限和动理学方程的分析。