The subleading order of two dimensional cover times
Probability
2014-05-06 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1405.0888,
title = {The subleading order of two dimensional cover times},
author = {David Belius and Nicola Kistler},
journal= {arXiv preprint arXiv:1405.0888},
year = {2014}
}
Comments
72 pages, 6 figures