{
  "id": "1010.2483",
  "version": "v2",
  "published": "2010-10-12T19:44:21.000Z",
  "updated": "2011-07-09T21:06:00.000Z",
  "title": "Logarithmic fluctuations for internal DLA",
  "authors": [
    "David Jerison",
    "Lionel Levine",
    "Scott Sheffield"
  ],
  "comment": "38 pages, 5 figures, v2 addresses referee comments. To appear in Journal of the AMS",
  "journal": "J. Amer. Math. Soc. 25 (2012), 271-301",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech"
  ],
  "abstract": "Let each of n particles starting at the origin in Z^2 perform simple random walk until reaching a site with no other particles. Lawler, Bramson, and Griffeath proved that the resulting random set A(n) of n occupied sites is (with high probability) close to a disk B_r of radius r=\\sqrt{n/\\pi}. We show that the discrepancy between A(n) and the disk is at most logarithmic in the radius: i.e., there is an absolute constant C such that the following holds with probability one: B_{r - C \\log r} \\subset A(\\pi r^2) \\subset B_{r+ C \\log r} for all sufficiently large r.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-09T21:06:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60K35",
      "82C24"
    ],
    "keywords": [
      "internal dla",
      "logarithmic fluctuations",
      "perform simple random walk",
      "absolute constant",
      "resulting random set"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "J. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.2483J"
    }
  }
}