{
  "id": "0707.0818",
  "version": "v1",
  "published": "2007-07-05T15:50:06.000Z",
  "updated": "2007-07-05T15:50:06.000Z",
  "title": "The number of open paths in an oriented $ρ$-percolation model",
  "authors": [
    "Francis Comets",
    "Serguei Popov",
    "Marina Vachkovskaia"
  ],
  "comment": "30 pages, 2 figures",
  "journal": "Journal of Statistical Physics, v. 131, p. 357-379, 2008",
  "doi": "10.1007/s10955-008-9506-2",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the asymptotic properties of the number of open paths of length $n$ in an oriented $\\rho$-percolation model. We show that this number is $e^{n\\alpha(\\rho)(1+o(1))}$ as $n \\to \\infty$. The exponent $\\alpha$ is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitely computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is $n^{-1/2} W e^{n\\alpha(\\rho)}(1+o(1))$ for some nondegenerate random variable $W$. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-05T15:50:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37"
    ],
    "keywords": [
      "percolation model",
      "open paths",
      "random environment",
      "asymptotic properties",
      "polymer model"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2008,
      "month": "Apr",
      "volume": 131,
      "number": 2,
      "pages": 357
    },
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JSP...131..357C"
    }
  }
}