{
  "id": "1207.7230",
  "version": "v2",
  "published": "2012-07-31T13:02:12.000Z",
  "updated": "2013-12-04T23:52:59.000Z",
  "title": "Random walk on the high-dimensional IIC",
  "authors": [
    "Markus Heydenreich",
    "Remco van der Hofstad",
    "Tim Hulshof"
  ],
  "comment": "48 pages. Main difference with previous version: some proofs have been strengthened to work under milder assumptions. To appear in Commun. Math. Phys",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the asymptotic behavior the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by [26]. We do this by obtaining bounds on the effective resistance between the origin and the boundary of these Euclidean balls. We show that the geometric properties of long-range percolation clusters are significantly different from those of finite-range clusters. We also study the behavior of random walk on the backbone of the IIC and we prove that the Alexander-Orbach conjecture holds for the incipient infinite cluster in high dimensions, both for long-range percolation and for finite-range percolation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-04T23:52:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37",
      "82B43"
    ],
    "keywords": [
      "random walk",
      "high-dimensional iic",
      "incipient infinite cluster",
      "euclidean balls",
      "alexander-orbach conjecture holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.7230H"
    }
  }
}