Fluctuation results for size of the vacant set for random walks on discrete torus

2021/08/14 by Partha S. Dey, Partha Dey, Dey, Partha +2
Mathematics · Physics and Astronomy · #60F99 #60G50 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60F99 #msc:60G50

paper · pdf · doi:10.48550/arxiv.2108.06450

25 pages, 1 figure

arxiv created 2021/08/14 · openalex publication_date 2021/08/14 · arxiv updated 2021/08/17 · openalex created_date 2021/08/30 · openalex updated_date 2026/07/28

Abstract

We consider one or more independent random walks on the d≥ 3 dimensional discrete torus. The walks start from vertices chosen independently and uniformly at random. We analyze the fluctuation behavior of the size of some random sets arising from the trajectories of the random walks at a time proportional to the size of the torus. Examples include vacant sets and the intersection of ranges. The proof relies on a refined analysis of tail estimates for hitting time and can be applied for other vertex-transitive graphs.

Citations

• On the range of random walk

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