報告人：葉文杰 博士
報告題目：Large N limit of the Langevin dynamics for the spin O(N) model
報告時間：2025年10月25日（周六）上午10：00
報告地點：云龍校區6號樓318會議室
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
葉文杰，上海交通大學博士畢業，現為福建師范大學講師，主要研究流形上的隨機分析，隨機控制以及倒向隨機微分方程，已在EJP,JTP等雜志上發表論文。
報告摘要：
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.