Extracting subsets maximizing capacity and Folding of Random Walks

2020/03/06 by Amine Asselah, Bruno Schapira, Asselah, Amine +1
Mathematics · #60F05 #60G50 #FOS: Mathematics #Limits and Structures in Graph Theory #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.2003.03073

openalex publication_date 2020/03/06 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We prove that in any finite set of \mathbb Z^d with d≥ 3, there is a subset whose capacity and volume are both of the same order as the capacity of the initial set. As an application we obtain estimates on the probability of \it covering uniformly a finite set, and characterize some \it folding events, under optimal hypotheses. For instance, knowing that a region of space has an \it atypically high occupation density by some random walk, we show that this random region is most likely ball-like

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