{
  "id": "0712.1497",
  "version": "v1",
  "published": "2007-12-10T14:48:46.000Z",
  "updated": "2007-12-10T14:48:46.000Z",
  "title": "How universal are asymptotics of disconnection times in discrete cylinders?",
  "authors": [
    "Alain-Sol Sznitman"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/009117907000000114 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2008, Vol. 36, No. 1, 1-53",
  "doi": "10.1214/009117907000000114",
  "categories": [
    "math.PR"
  ],
  "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 $G_N\\times\\mathbb{Z}$ has rough order $|G_N|^2$, when $G_N=(\\mathbb{Z}/N\\mathbb{Z})^d$. 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-10T14:48:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60K35",
      "82C41"
    ],
    "keywords": [
      "disconnection time",
      "discrete cylinder",
      "asymptotics",
      "large finite connected base",
      "simple random walk"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.1497S"
    }
  }
}