Second order term of cover time for planar simple random walk
Probability
2020-04-21 v3
Abstract
We consider the cover time for a simple random walk on the two-dimensional discrete torus of side length . Dembo, Peres, Rosen, and Zeitouni [Ann. Math. 160:433-464, 2004] identified the leading term in the asymptotics for the cover time as goes to infinity. In this paper, we study the exact second order term. This is a discrete analogue of the work on the cover time for planar Brownian motion by Belius and Kistler [Probab. Theory Relat Fields. 167:461-552, 2017].
Keywords
Cite
@article{arxiv.1709.08151,
title = {Second order term of cover time for planar simple random walk},
author = {Yoshihiro Abe},
journal= {arXiv preprint arXiv:1709.08151},
year = {2020}
}
Comments
56 pages; to appear in Journal of Theoretical Probability