{
  "id": "0809.1712",
  "version": "v1",
  "published": "2008-09-10T05:55:17.000Z",
  "updated": "2008-09-10T05:55:17.000Z",
  "title": "Convergence of the critical finite-range contact process to super-Brownian motion above the upper critical dimension: I. The higher-point functions",
  "authors": [
    "Remco van der Hofstad",
    "Akira Sakai"
  ],
  "comment": "75 pages, 12 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the critical spread-out contact process in Z^d with d\\ge1, whose infection range is denoted by L\\ge1. In this paper, we investigate the r-point function \\tau_{\\vec t}^{(r)}(\\vec x) for r\\ge3, which is the probability that, for all i=1,...,r-1, the individual located at x_i\\in Z^d is infected at time t_i by the individual at the origin o\\in Z^d at time 0. Together with the results of the 2-point function in [van der Hofstad and Sakai, Electron. J. Probab. 9 (2004), 710-769; arXiv:math/0402049], on which our proofs crucially rely, we prove that the r-point functions converge to the moment measures of the canonical measure of super-Brownian motion above the upper-critical dimension 4. We also prove partial results for d\\le4 in a local mean-field setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-10T05:55:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B27",
      "82B43"
    ],
    "keywords": [
      "critical finite-range contact process",
      "upper critical dimension",
      "super-brownian motion",
      "higher-point functions",
      "convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 75,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.1712V"
    }
  }
}