报告人：叶文杰 博士
报告题目：Large N limit of the Langevin dynamics for the spin O(N) model
报告时间：2025年10月25日（周六）上午10：00
报告地点：云龙校区6号楼318会议室
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
叶文杰，上海交通大学博士毕业，现为福建师范大学讲师，主要研究流形上的随机分析，随机控制以及倒向随机微分方程，已在EJP,JTP等杂志上发表论文。
报告摘要：
In this paper, we prove that the large N limit of the Langevin dynamics for the spin O(N) model is given by a mean-field stochastic differential equation (SDE) in both finite and infinite volumes. We establish uniform in N bounds for the dynamics, which enable us to demonstrate convergence to the mean-field SDE with polynomial interactions. Furthermore, the mean-field SDE is shown to be globally well-posed for suitable initial distributions. We also prove the existence of stationary measures for the mean-field SDE. For small inverse temperatures, we characterize the large N limit of the spin O(N) model through stationary coupling. Additionally, we establish the uniqueness of the stationary measure for the mean-field SDE.
