The Annals of Probability

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 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.

Article information

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

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1196268672

Digital Object Identifier
doi:10.1214/009117907000000114

Mathematical Reviews number (MathSciNet)
MR2370597

Zentralblatt MATH identifier
1134.60061

Subjects
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]

Keywords
Disconnection time random walks on graphs discrete cylinders

Citation

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. https://projecteuclid.org/euclid.aop/1196268672


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