The Annals of Probability
- Ann. Probab.
- Volume 36, Number 1 (2008), 1-53.
How universal are asymptotics of disconnection times in discrete cylinders?
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.
Ann. Probab., Volume 36, Number 1 (2008), 1-53.
First available in Project Euclid: 28 November 2007
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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]
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