{
  "id": "math/0703455",
  "version": "v2",
  "published": "2007-03-15T15:12:42.000Z",
  "updated": "2007-08-21T18:01:05.000Z",
  "title": "Critical behavior and the limit distribution for long-range oriented percolation. I",
  "authors": [
    "Lung-Chi Chen",
    "Akira Sakai"
  ],
  "comment": "33 pages, 2 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider oriented percolation on Z^d times Z_+ whose bond-occupation probability is pD(...), where p is the percolation parameter and D is a probability distribution on Z^d. Suppose that D(x) decays as |x|^{-d-\\alpha} for some \\alpha>0. We prove that the two-point function obeys an infrared bound which implies that various critical exponents take on their respective mean-field values above the upper-critical dimension 2\\min{\\alpha,2}. We also show that, for every k, the Fourier transform of the normalized two-point function at time n, with a proper spatial scaling, has a convergent subsequence to exp(-c|k|^{\\min{\\alpha,2}}) for some c>0.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-21T18:01:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B27"
    ],
    "keywords": [
      "long-range oriented percolation",
      "limit distribution",
      "critical behavior",
      "two-point function obeys",
      "convergent subsequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3455C"
    }
  }
}