Couplings, Strong Invariance Principles with Applications to Random Walks on Inifinite Percolation Clusters

Speaker: 苏中根 博士, 浙江大学

Title: Couplings, Strong Invariance Principles with Applications to Random Walks on Inifinite Percolation Clusters

Time & Venue: 2025 年9月19日14:00–15:00 南楼613

Abstract: This talk basically consists of two parts. First, I will briefly review some classical coupling methods and strong invariance principles for sums of independent random variables in probability theory. Then I will report a recent work on couplings between Brownian motions and random walks on the infinite cluster in the supercritical Bernoulli bond percolation on $\mathbb{Z}^d$. As a corollary, we recover the law of the iterated logarithm proved by Duminil-Copin (arXiv:0809.4380) and further identify the limit constant. This talk is mainly based on a joint work with C.Gu and R. Xu (PTRF, 2025).