{
  "id": "1404.2118",
  "version": "v1",
  "published": "2014-04-08T13:24:01.000Z",
  "updated": "2014-04-08T13:24:01.000Z",
  "title": "Large deviation bounds for the volume of the largest cluster in 2D critical percolation",
  "authors": [
    "Demeter Kiss"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let M_n denote the number of sites in the largest cluster in critical site percolation on the triangular lattice inside a box side length n. We give lower and upper bounds on the probability that M_n / E(M_n) > x of the form exp(- C x^(2/alpha)) for x > 1 and large n with alpha = 5/48 and C > 0. Our results extend to other two dimensional lattices and strengthen the previously known exponential upper bound derived by Borgs, Chayes, Kesten and Spencer [BCKS99]. Furthermore, under some general assumptions similar to those in [BCKS99], we derive a similar upper bound in dimensions d > 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-08T13:24:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "large deviation bounds",
      "2d critical percolation",
      "largest cluster",
      "exponential upper bound",
      "triangular lattice inside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.2118K"
    }
  }
}