{
  "id": "0708.4369",
  "version": "v1",
  "published": "2007-08-31T15:24:37.000Z",
  "updated": "2007-08-31T15:24:37.000Z",
  "title": "The size of a pond in 2D invasion percolation",
  "authors": [
    "Jacob van den Berg",
    "Antal A. Járai",
    "Bálint Vágvölgyi"
  ],
  "comment": "11 pages",
  "journal": "Electron. Comm. Probab. 12 (2007), 411-420",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider invasion percolation on the square lattice. It has been proved by van den Berg, Peres, Sidoravicius and Vares, that the probability that the radius of a so-called pond is larger than n, differs at most a factor of order log n from the probability that in critical Bernoulli percolation the radius of an open cluster is larger than n. We show that these two probabilities are, in fact, of the same order. Moreover, we prove an analogous result for the volume of a pond.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-31T15:24:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "2d invasion percolation",
      "van den berg",
      "probability",
      "square lattice",
      "order log"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.4369V"
    }
  }
}