Large Deviation Principle for Empirical Measures of Once-reinforced Random Walks on Finite Graphs
报告专家:刘勇 教授（北京大学）
报告时间:9月16日（星期五）10:00-11:00
报告地点:腾讯会议：735-399-773（0916）
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.
专家简介：
刘勇，北京大学数学学院教授。 1999年在北京大学数学学院获得博士学位，随后在中国科学院数学与系统科学研究院做博士后。主要研究兴趣是大偏差理论，随机分析和随机偏微分方程。
