How universal are asymptotics of disconnection times in discrete cylinders?

Details How universal are asymptotics of disconnection times in discrete cylinders? How universal are asymptotics of disconnection times in discrete cylinders?

2007-12-10

arxiv.org/abs/0712.1497v1

Annals of Probability 2008, Vol. 36, No. 1, 1-53

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/009117907000000114 the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117907000000114

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.

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