{
  "id": "math/0607253",
  "version": "v2",
  "published": "2006-07-11T11:10:23.000Z",
  "updated": "2007-03-26T12:19:28.000Z",
  "title": "Upper large deviations for the maximal flow in first passage percolation",
  "authors": [
    "Marie Théret"
  ],
  "comment": "27 pages, 4 figures; small changes of notations",
  "journal": "Stochastic Processes and their Applications, Volume 117, Issue 9, Septembre 2007, Pages 1208-1233",
  "doi": "10.1016/j.spa.2006.12.007",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the standard first passage percolation in $\\mathbb{Z}^{d}$ for $d\\geq 2$ and we denote by $\\phi_{n^{d-1},h(n)}$ the maximal flow through the cylinder $]0,n]^{d-1} \\times ]0,h(n)]$ from its bottom to its top. Kesten proved a law of large numbers for the maximal flow in dimension three: under some assumptions, $\\phi_{n^{d-1},h(n)} / n^{d-1}$ converges towards a constant $\\nu$. We look now at the probability that $\\phi_{n^{d-1},h(n)} / n^{d-1}$ is greater than $\\nu + \\epsilon$ for some $\\epsilon >0$, and we show under some assumptions that this probability decays exponentially fast with the volume of the cylinder. Moreover, we prove a large deviations principle for the sequence $(\\phi_{n^{d-1},h(n)} / n^{d-1}, n\\in \\mathbb{N})$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-03-26T12:19:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "upper large deviations",
      "maximal flow",
      "standard first passage percolation",
      "probability decays exponentially fast",
      "large deviations principle"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7253T"
    }
  }
}