{
  "id": "0909.4422",
  "version": "v1",
  "published": "2009-09-24T12:23:54.000Z",
  "updated": "2009-09-24T12:23:54.000Z",
  "title": "Upper bound on the disconnection time of discrete cylinders and random interlacements",
  "authors": [
    "Alain-Sol Sznitman"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AOP450 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2009, Vol. 37, No. 5, 1715-1746",
  "doi": "10.1214/09-AOP450",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the asymptotic behavior for large $N$ of the disconnection time $T_N$ of a simple random walk on the discrete cylinder $(\\mathbb{Z}/N\\mathbb{Z})^d\\times\\mathbb{Z}$, when $d\\ge2$. We explore its connection with the model of random interlacements on $\\mathbb{Z}^{d+1}$ recently introduced in [Ann. Math., in press], and specifically with the percolative properties of the vacant set left by random interlacements. As an application we show that in the large $N$ limit the tail of $T_N/N^{2d}$ is dominated by the tail of the first time when the supremum over the space variable of the Brownian local times reaches a certain critical value. As a by-product, we prove the tightness of the laws of $T_N/N^{2d}$, when $d\\ge2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-24T12:23:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60K35",
      "82C41"
    ],
    "keywords": [
      "random interlacements",
      "discrete cylinder",
      "disconnection time",
      "upper bound",
      "brownian local times reaches"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4422S"
    }
  }
}