报告题目 (Title)：Exponential Ergodicity for McKean-Vlasov SDEs with Singular Interactions（具有奇异相互作用的McKean-Vlasov随机微分方程的指数遍历性）
报告人 (Speaker)：黄兴 教授（天津大学）
报告时间 (Time)：2025年11月14日（周五）19：00-22:00
报告地点 (Place)： 腾讯会议：880-966-912
邀请人(Inviter)：阳芬芬
主办部门：理学院数学系
报告摘要：Let $k\in (d,\infty]$ and consider the $k*$-distance $$\|\mu-\nu\|_{k*}:= \sup\Big\{|\mu(f)-\nu(f)|:\ f\in\B_b(\R^d),\ \|f\|_{\tt L^k}:=\sup_{x\in \R^d}\|1_{B(x,1)}f\|_{L^k}\le 1\Big\}$$
between probability measures on $\R^d$. The exponential ergodicity in $1$-Wasserstein and $k*$-distances is derived for a class of McKean-Vlasov SDEs with small singular interactions measured by $\|\cdot\|_{k*}.$ Moreover, the exponential ergodicity in $2$-Wasserstein distance and relative entropy is derived when the interaction term is given by
$$b^{(0)}(x,\mu) :=\int_{\R^d}h(x-y)\mu(\d y)$$ for some measurable function $h:\R^d\to\R^d$ with small $\|h\|_{\tt L^k}$.
