On the disconnection of a discrete cylinder by a biased random walk

dc.creatorWindisch, David
dc.date2007-10-24
dc.date2008-08-21
dc.date.accessioned2026-07-07T09:57:24Z
dc.date.available2026-07-07T09:57:24Z
dc.descriptionWe consider a random walk on the discrete cylinder $({\mathbb{Z}}/N{\mathbb{Z}})^d\times{\mathbb{Z}}$, $d\geq3$ with drift $N^{-dα}$ in the $\mathbb{Z}$-direction and investigate the large $N$-behavior of the disconnection time $T^{\mathrm{disc}}_N$, defined as the first time when the trajectory of the random walk disconnects the cylinder into two infinite components. We prove that, as long as the drift exponent $α$ is strictly greater than 1, the asymptotic behavior of $T^{\mathrm{disc}}_N$ remains $N^{2d+o(1)}$, as in the unbiased case considered by Dembo and Sznitman, whereas for $α<1$, the asymptotic behavior of $T^{\mathrm{disc}}_N$ becomes exponential in $N$.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AAP491 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0710.4427
dc.identifierhttp://arxiv.org/abs/0710.4427
dc.identifierAnnals of Applied Probability 2008, Vol. 18, No. 4, 1441-1490
dc.identifierdoi:10.1214/07-AAP491
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167330
dc.subjectProbability
dc.subject60G50 (Primary)
dc.titleOn the disconnection of a discrete cylinder by a biased random walk
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