概率论系列报告（讨论班）—ON COVERING MONOTONIC PATHS WITH SIMPLE RANDOM WALK
主 题: 概率论系列报告（讨论班）—ON COVERING MONOTONIC PATHS WITH SIMPLE RANDOM WALK
报告人: 张原 博士 (Texas AandM University)
时 间: 2017-05-29 15:00-16:00
地 点: 理科1号楼1303
Abstract: In this paper we study the probability that a $d$ dimensional simple random walk (or the first $L$ steps of it) covers each point in a nearest neighbor path connecting 0 and the boundary of an $L_1$ ball. We show that among all such paths, the one that maximizes the covering probability is the monotonic increasing one that stays within distance 1 from the diagonal. As a result, we can obtain an exponential upper bound on the decaying rate of covering probability of any such path when $d\ge 4$.