{
  "id": "math/0609826",
  "version": "v1",
  "published": "2006-09-28T22:07:05.000Z",
  "updated": "2006-09-28T22:07:05.000Z",
  "title": "Probability of hitting a distant point for the voter model started with a single one",
  "authors": [
    "Mathieu Merle"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The goal of this work is to find the asymptotics of the hitting probability of a distant point for the voter model on the integer lattice started from a single 1 at the origin. In dimensions 2 or 3, we obtain the precise asymptotic behavior of this probability. We use the scaling limit of the voter model started from a single 1 at the origin in terms of super-Brownian motion under its excursion measure. This invariance principle was stated by Bramson, Cox and Le Gall, as a consequence of a theorem of Cox, Durrett and Perkins. Less precise estimates are derived in dimensions greater than 4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-28T22:07:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K30",
      "60J80",
      "60F17",
      "60G57"
    ],
    "keywords": [
      "voter model",
      "distant point",
      "probability",
      "precise asymptotic behavior",
      "precise estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9826M"
    }
  }
}