2017/04/19 by Eviatar B. Procaccia, Yuan Zhang, Procaccia, Eviatar B. +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1704.05870
openalex publication_date 2017/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 L1 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≥ 4.