2011/03/10 by David Belius, Belius, David
Mathematics · #60D05 #60G50 #82C41 #FOS: Mathematics #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60D05 #msc:60G50 #msc:82C41
paper · pdf · doi:10.48550/arxiv.1103.2079
39 pages
arxiv created 2011/03/10 · openalex publication_date 2011/03/10 · arxiv updated 2011/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article proves that, in terms of local times, the rescaled and recentered cover times of finite subsets of the discrete cylinder by simple random walk converge in law to the Gumbel distribution, as the cardinality of the set goes to infinity. As applications we obtain several other results related to covering in the discrete cylinder. Our method is new and involves random interlacements, which were introduced by Sznitman in arXiv:0704.2560. To enable the proof we develop a new stronger coupling of simple random walk in the cylinder and random interlacements, which is also of independent interest.