{
  "id": "1405.7606",
  "version": "v1",
  "published": "2014-05-29T16:22:14.000Z",
  "updated": "2014-05-29T16:22:14.000Z",
  "title": "The dimension of the Incipient Infinite Cluster",
  "authors": [
    "Wouter Cames van Batenburg"
  ],
  "comment": "9 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the Incipient Infinite Cluster (IIC) of high-dimensional bond percolation on $\\mathbb{Z}^d$. We prove that the mass dimension of IIC almost surely equals $4$ and the volume growth exponent of IIC almost surely equals $2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-29T16:22:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "incipient infinite cluster",
      "volume growth exponent",
      "high-dimensional bond percolation",
      "surely equals",
      "mass dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.7606C"
    }
  }
}