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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:20221219 15:00--16:00


方式:腾讯会议  ID137 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 rst 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 dierentiable 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