{
  "id": "0907.5501",
  "version": "v1",
  "published": "2009-07-31T10:40:45.000Z",
  "updated": "2009-07-31T10:40:45.000Z",
  "title": "Lower large deviations for the maximal flow through a domain of $\\mathbb{R}^d$ in first passage percolation",
  "authors": [
    "Raphaël Cerf",
    "Marie Théret"
  ],
  "comment": "23 pages, 8 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the standard first passage percolation model in the rescaled graph $\\mathbb{Z}^d/n$ for $d\\geq 2$, 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 behaviour 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 lower large deviations of $\\phi_n/ n^{d-1}$ below a certain constant are of surface order.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-31T10:40:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "lower large deviations",
      "maximal flow",
      "standard first passage percolation model",
      "disjoint open subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.5501C"
    }
  }
}