The Annals of Probability

How universal are asymptotics of disconnection times in discrete cylinders?

Alain-Sol Sznitman

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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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Ann. Probab., Volume 36, Number 1 (2008), 1-53.

First available in Project Euclid: 28 November 2007

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Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]

Disconnection time random walks on graphs discrete cylinders


Sznitman, Alain-Sol. How universal are asymptotics of disconnection times in discrete cylinders?. Ann. Probab. 36 (2008), no. 1, 1--53. doi:10.1214/009117907000000114.

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