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arXiv · 0712.1497

How universal are asymptotics of disconnection times in discrete cylinders?

Alain-Sol Sznitman
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Abstract

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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Alain-Sol Sznitman. 2007-12-10. How universal are asymptotics of disconnection times in discrete cylinders?. https://doi.org/10.1214/009117907000000114

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