报告题目：Sequential Interacting Diffusions: Convergence and Fluctuations

报 告 人：赵显亮 博士后（北京大学北京国际数学研究中心）

报告时间：2026年6月25日（星期四）9：00—10：00

报告地点：数学科学学院114（小报告厅）          

校内联系人： 程梦雨 副教授 联系方式：84708351-8206

报告摘要：I will discuss a directed, non-exchangeable particle approximation of McKean-Vlasov diffusions, where particle \(i\) interacts only with its predecessors through their empirical measure. Although the system has the same McKean-Vlasov limit as the classical exchangeable model, its sequential structure leads to different quantitative and fluctuation behavior.

The first part concerns propagation of chaos via an incremental path-space relative entropy, giving sharp \((i-1)^{-1}\) one-step entropy estimates and \(N^{-1/2}\)-scale empirical convergence in negative Sobolev norms. A key ingredient is the construction of auxiliary random measures from conditional laws, which replace predecessor empirical measures by averaged conditional measures. The second part presents a central limit theorem: the limiting averaged fluctuation is Gaussian, but its equation is coupled to a hierarchy of logarithmically weighted fluctuation fields.

报告人简介：赵显亮，2023年获德国 Bielefeld University 数学博士学位，现为北京大学北京国际数学研究中心博士后。主要研究方向为随机分析与相互作用粒子系统，研究兴趣集中在奇异相互作用粒子系统的极限理论，包括平均场极限、高斯涨落及大偏差估计等。相关工作发表于 Arch. Ration. Mech. Anal.、 SIAM J. Math. Anal.等期刊。