## The Annals of Probability

### How universal are asymptotics of disconnection times in discrete cylinders?

Alain-Sol Sznitman

#### 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

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

Digital Object Identifier
doi:10.1214/009117907000000114

Mathematical Reviews number (MathSciNet)
MR2370597

Zentralblatt MATH identifier
1134.60061

#### 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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