English

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 nn. Dembo, Peres, Rosen, and Zeitouni [Ann. Math. 160:433-464, 2004] identified the leading term in the asymptotics for the cover time as nn 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

R2 v1 2026-06-22T21:52:56.319Z