A Lower Bound on the Disconnection Time of a Discrete Cylinder
Probability
2008-07-28 v2 Mathematical Physics
math.MP
Abstract
We study the asymptotic behavior for large N of the disconnection time T_N of simple random walk on a discrete cylinder with base a d-dimensional discrete torus of side-length N. When d is sufficiently large, we are able to substantially improve the lower bounds obtained by the authors in a previous article when d is bigger or equal to 2. We show here that the laws of N^(2d)/T_N are tight.
Keywords
Cite
@article{arxiv.math/0701414,
title = {A Lower Bound on the Disconnection Time of a Discrete Cylinder},
author = {Amir Dembo and Alain-Sol Sznitman},
journal= {arXiv preprint arXiv:math/0701414},
year = {2008}
}
Comments
17 pages, this article appears in the volume In and Out of Equilibrium 2, V. Sidoravicius and M. E. Vares Editors