How universal are asymptotics of disconnection times in discrete cylinders?

Date
Authors
Sznitman, Alain-Sol
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
We investigate the disconnection time of a simple random walk in a discrete cylinder with a large finite connected base. In a recent article of A. Dembo and the author it was found that for large $N$ the disconnection time of $G_N\times\mathbb{Z}$ has rough order $|G_N|^2$, when $G_N=(\mathbb{Z}/N\mathbb{Z})^d$. In agreement with a conjecture by I. Benjamini, we show here that this behavior has broad generality when the bases of the discrete cylinders are large connected graphs of uniformly bounded degree.
Comment: Published in at http://dx.doi.org/10.1214/009117907000000114 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Keywords
Mathematics - Probability, 60J10, 60K35, 82C41 (Primary)
Citation
Collections