{
  "id": "1005.5696",
  "version": "v4",
  "published": "2010-05-31T15:29:06.000Z",
  "updated": "2014-07-03T16:58:33.000Z",
  "title": "Limit theorems for 2D invasion percolation",
  "authors": [
    "Michael Damron",
    "Artëm Sapozhnikov"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/10-AOP641 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org). Note: the statement of Lemma 3 (which is Theorem 2.1 in Withers (1981)) should include the condition liminf_n b_n^2/n > 0, which is valid in our setting. See the corrigendum to Theorem 2.1 in Withers (1983) in Z. Wahrsch",
  "journal": "Annals of Probability 2012, Vol. 40, No. 3, 893-920",
  "doi": "10.1214/10-AOP641",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove limit theorems and variance estimates for quantities related to ponds and outlets for 2D invasion percolation. We first exhibit several properties of a sequence $({\\mathbf{O}}(n))$ of outlet variables, the $n$th of which gives the number of outlets in the box centered at the origin of side length $2^n$. The most important of these properties describes the sequence's renewal structure and exponentially fast mixing behavior. We use these to prove a central limit theorem and strong law of large numbers for $({\\mathbf{O}}(n))$. We then show consequences of these limit theorems for the pond radii and outlet weights.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-07-03T16:58:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "2d invasion percolation",
      "sequences renewal structure",
      "central limit theorem",
      "properties",
      "side length"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.5696D"
    }
  }
}