Open Access
January 2008 How universal are asymptotics of disconnection times in discrete cylinders?
Alain-Sol Sznitman
Ann. Probab. 36(1): 1-53 (January 2008). DOI: 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 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.


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Alain-Sol Sznitman. "How universal are asymptotics of disconnection times in discrete cylinders?." Ann. Probab. 36 (1) 1 - 53, January 2008.


Published: January 2008
First available in Project Euclid: 28 November 2007

zbMATH: 1134.60061
MathSciNet: MR2370597
Digital Object Identifier: 10.1214/009117907000000114

Primary: 60J10 , 60K35 , 82C41

Keywords: Disconnection time , discrete cylinders , random walks on graphs

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 1 • January 2008
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