報(bào)告人：葉文杰 博士

報(bào)告題目：Large N limit of the Langevin dynamics for the spin O(N) model

報(bào)告時(shí)間：2025年10月25日（周六）上午10：00

報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓318會(huì)議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

葉文杰，上海交通大學(xué)博士畢業(yè)，現(xiàn)為福建師范大學(xué)講師，主要研究流形上的隨機(jī)分析，隨機(jī)控制以及倒向隨機(jī)微分方程，已在EJP,JTP等雜志上發(fā)表論文。

報(bào)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.