Gumbel fluctuations for cover times in the discrete torus
Probability
2012-11-08 v2
Abstract
This work proves that the fluctuations of the cover time of simple random walk in the discrete torus of dimension at least three with large side-length are governed by the Gumbel extreme value distribution. This result was conjectured for example in the book by Aldous & Fill. We also derive some corollaries which qualitatively describe "how" covering happens. In addition, we develop a new and stronger coupling of the model of random interlacements, introduced by Sznitman, and random walk in the torus. This coupling is used to prove the cover time result and is also of independent interest.
Keywords
Cite
@article{arxiv.1202.0190,
title = {Gumbel fluctuations for cover times in the discrete torus},
author = {David Belius},
journal= {arXiv preprint arXiv:1202.0190},
year = {2012}
}
Comments
41 pages. Accepted for publication in Probability Theory and Related Fields