{
  "id": "0907.5499",
  "version": "v2",
  "published": "2009-07-31T10:44:54.000Z",
  "updated": "2012-02-17T07:35:12.000Z",
  "title": "Upper large deviations for the maximal flow through a domain of $\\bolds{\\mathbb{R}^d}$ in first passage percolation",
  "authors": [
    "Raphaël Cerf",
    "Marie Théret"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/10-AAP732 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 2011, Vol. 21, No. 6, 2075-2108",
  "doi": "10.1214/10-AAP732",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the standard first passage percolation model in the rescaled graph $\\mathbb {Z}^d/n$ for $d\\geq2$ and a domain $\\Omega$ of boundary $\\Gamma$ in $\\mathbb {R}^d$. Let $\\Gamma ^1$ and $\\Gamma ^2$ be two disjoint open subsets of $\\Gamma$ representing the parts of $\\Gamma$ through which some water can enter and escape from $\\Omega$. We investigate the asymptotic behavior of the flow $\\phi_n$ through a discrete version $\\Omega_n$ of $\\Omega$ between the corresponding discrete sets $\\Gamma ^1_n$ and $\\Gamma ^2_n$. We prove that under some conditions on the regularity of the domain and on the law of the capacity of the edges, the upper large deviations of $\\phi_n/n^{d-1}$ above a certain constant are of volume order, that is, decays exponentially fast with $n^d$. This article is part of a larger project in which the authors prove that this constant is the a.s. limit of $\\phi_n/n^{d-1}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-17T07:35:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "upper large deviations",
      "maximal flow",
      "standard first passage percolation model",
      "disjoint open subsets"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.5499C"
    }
  }
}