报告题目: Mean Field Behavior during the Big Bang regime for Coalescing Random Walks
时 间：2023年5月23日（星期二）上午10:30
地 点：理工南楼618
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：The talk is concerned with the coalescing random walk model on general graphs G. Initially every vertex of G has a particle. Each particle performs independent random walks. Whenever two particles meet, they merge into one particle which continues to perform a random walk. We set up a unified framework to study the leading order of the decay rate of P(t), which is the expectation of the fraction of occupied sites at time t, particularly for the ‘Big Bang’ regime where the time t<< T(coal):=E[inf{s: There is only one particle left at time s}].
Our results show that P(t) satisfies certain `mean field behavior', if the graphs satisfy certain ‘transience-like’ conditions. We apply this framework to two families of graphs: (1) graphs generated by configuration model with degree at least 3, and (2) finite and infinite vertex-transitive graphs. In the first case, (tP(t))^{-1} is approximately the probability that two particles starting from the root of the corresponding unimodular Galton-Watson tree never collide after one of them leaves the root. In the second case we establish similar results for finite ‘uniformly transient’ graphs and infinite transient transitive unimodular graphs. Based on joint work with Jonathan Hermon, Shuangping Li and Lingfu Zhang.
报告人简介：姚东，江苏师范大学数学研究院副教授。2021年9月博士毕业于美国杜克大学，师从Rick Durrett教授，研究方向为概率论与生物数学。已在AOP,EJP等概率权威期刊发表论文。