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【online】Large Deviation Principle for Empirical Measures of Once-reinforced Random ......

发布人：发布时间： 2022-12-16

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**题目：**Large Deviation Principle for Empirical Measures of Once-reinforced Random Walks on Finite Graphs

**报告人：**刘勇 教授（北京大学）

**时间：**2022年12月19日 15:00--16:00

**方式：**腾讯会议 ID：137 108 871

**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.

**邀请人：**宋玉林 老师