报告题目: A stochastic analysis approach to lattice Yang--Mills
时 间：2022年10月18日（星期二）上午9：30-11：30
地 点：腾讯会议（ID：621-690-454）
主 办：数学与统计学院
参加对象：统计系老师与学生
报告摘要：We develop a new stochastic analysis approach to the lattice Yang--Mills model at strong coupling in any dimension $d>1$, with t' Hooft scaling $\beta N$ for the inverse coupling strength. We study their Langevin dynamics, ergodicity, functional inequalities, large $N$ limits, and mass gap. Assuming $|\beta| < \frac{N-2}{32(d-1)N}$ for the structure group $SO(N)$, or $|\beta| < \frac{1}{16(d-1)}$ for $SU(N)$, we prove the following results. The invariant measure for the corresponding Langevin dynamic is unique on the entire lattice, and the dynamic is exponentially ergodic under a Wasserstein distance. The finite volume Yang--Mills measures converge to this unique invariant measure in the infinite volume limit, for which Log-Sobolev and Poincar\'e inequalities hold. These functional inequalities imply that the suitably rescaled Wilson loops for the infinite volume measure has factorized correlations and converges in probability to deterministic limits in the large $N$ limit, and correlations of a large class of observables decay exponentially, namely the infinite volume measure has a strictly positive mass gap. Our method improves earlier results or simplifies the proofs, and provides some new perspectives to the study of lattice Yang--Mills model.
报告人简介：朱蓉禅，北京理工大学教授，主要从事随机偏微分方程，随机分析，狄氏型理论等相关研究。目前主要研究带有奇异噪声的随机偏微分方程和随机流体方程。2012年博士毕业于中国科学院数学与系统科学研究院和德国比勒菲尔德大学。2019年获国家自然科学基金优秀青年基金项目。在AOP，CMP，JFA，JDE等期刊上发表多篇论文。