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 GN×ℤ has rough order |GN|2, when GN=(ℤ/Nℤ)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.
Citation
Alain-Sol Sznitman. "How universal are asymptotics of disconnection times in discrete cylinders?." Ann. Probab. 36 (1) 1 - 53, January 2008. https://doi.org/10.1214/009117907000000114
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