2014/05/05 by David Belius, Belius, David, Nicola Kistler +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60J65 82C41 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60J65 #msc:82C41
paper · pdf · doi:10.48550/arxiv.1405.0888
72 pages, 6 figures
arxiv created 2014/05/05 · openalex publication_date 2014/05/05 · arxiv updated 2014/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The epsilon-cover time of the two dimensional torus by Brownian motion is the time it takes for the process to come within distance epsilon>0 from any point. Its leading order in the small epsilon-regime has been established by Dembo, Peres, Rosen and Zeitouni [Ann. of Math., 160 (2004)]. In this work, the second order correction is identified. The approach relies on a multi-scale refinement of the second moment method, and draws on ideas from the study of the extremes of branching Brownian motion.