{
  "id": "0710.4427",
  "version": "v2",
  "published": "2007-10-24T11:13:27.000Z",
  "updated": "2008-08-21T04:56:34.000Z",
  "title": "On the disconnection of a discrete cylinder by a biased random walk",
  "authors": [
    "David Windisch"
  ],
  "comment": "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)",
  "journal": "Annals of Applied Probability 2008, Vol. 18, No. 4, 1441-1490",
  "doi": "10.1214/07-AAP491",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a random walk on the discrete cylinder $({\\mathbb{Z}}/N{\\mathbb{Z}})^d\\times{\\mathbb{Z}}$, $d\\geq3$ with drift $N^{-d\\alpha}$ 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 $\\alpha$ 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 $\\alpha<1$, the asymptotic behavior of $T^{\\mathrm{disc}}_N$ becomes exponential in $N$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-08-21T04:56:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50"
    ],
    "keywords": [
      "biased random walk",
      "discrete cylinder",
      "asymptotic behavior",
      "random walk disconnects",
      "disconnection time"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.4427W"
    }
  }
}