报告题目：Quantitative PoC and Fluctuation for kinetic MV-SDEs with singular interaction kernels

报告人：张希承 北京理工大学

报告时间：10月23日 10:00

报告地点：新楼308

摘要：

We prove the quantitative propagation of chaos and central limit theorems for the particle system associated with a class of degenerate kinetic McKean--Vlasov SDEs with external drifts and singular interaction kernels in Kato's class. In particular, the interaction kernel can be in the mixed $L^q_tL^{p_x}_xL^{p_v}_v$-space, where $\frac2q+\frac{3d}{p_x}+\frac d{p_v}<1$. For the associated $N$-particle system, we obtain a path-space relative entropy bound of order $k/N$ for the first $k$ particles, assuming only entropic chaoticity of the initial data, where the key points are the kinetic Krylov--Khasminskii estimates, and a conditional Hilbert-space subgaussian estimate for empirical interaction fields. For the CLT, we also show a Berry-Esseen's type bound for the finite dimensional projection. (This is a joint work with Zimo Hao and Xianliang Zhao.)