报告人：刘勇
报告地点：腾讯会议ID:427 718 000
报告时间：2022年10月05日星期三10:00-11:00
报告摘要：
The once-reinforced random walk (ORRW) is a kind of non-Markov process with the transition probability only depending on the current weights of all edges. The weights are set to be 1 initially. At the first time an edge is traversed, its weight is changed to a positive parameter δ at once, and it will remain in δ. We introduce a log-transforms of exponential moments of restricted empirical measure functionals, and prove a variational formula for the limit of the functionals through a variational representation given by a novel dynamic programming equation associated with these functionals. As a corollary, we deduce the large deviation principle for the empirical measure of the ORRW. Its rate function is decreasing in δ, and is not differentiable at δ=1. Moreover, we characterize the critical exponent for the exponential integrability of a class of stopping times including the cover time and the hitting time. For the critical exponent, we show that it is continuous and strictly decreasing in δ, and describe a relationship between its limit (as δ→0) and the structure of the graph. This is a joint work with Dr. Xiangyu Huang and Professor Kainan Xiang.
主讲人简介：
刘勇，北京大学数学学院教授、博士生导师。1999年在北京大学数学学院获得博士学位，随后在中国科学与数学与系统科学研究院作博士后，在英国Loughborough大学数学系作Research Associate，受邀访问过剑桥大学Newton数学研究所，德国Weierstrass 研究所，美国 Kansas 大学数学系，日本东京大学数学系等学术机构。主要研究兴趣是大偏差理论，随机分析和随机偏微分方程.
