On the disconnection of a discrete cylinder by a biased random walk
| dc.creator | Windisch, David | |
| dc.date | 2007-10-24 | |
| dc.date | 2008-08-21 | |
| dc.date.accessioned | 2026-07-07T09:57:24Z | |
| dc.date.available | 2026-07-07T09:57:24Z | |
| dc.description | We 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.description | Published 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.identifier | https://arxiv.org/abs/0710.4427 | |
| dc.identifier | http://arxiv.org/abs/0710.4427 | |
| dc.identifier | Annals of Applied Probability 2008, Vol. 18, No. 4, 1441-1490 | |
| dc.identifier | doi:10.1214/07-AAP491 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167330 | |
| dc.subject | Probability | |
| dc.subject | 60G50 (Primary) | |
| dc.title | On the disconnection of a discrete cylinder by a biased random walk | |
| dc.type | text |