{
  "id": "math/0503118",
  "version": "v1",
  "published": "2005-03-07T06:05:53.000Z",
  "updated": "2005-03-07T06:05:53.000Z",
  "title": "Random walk on the incipient infinite cluster on trees",
  "authors": [
    "Martin T. Barlow",
    "Takashi Kumagai"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let ${\\cal G}$ be the incipient infinite cluster (IIC) for percolation on a homogeneous tree of degree $n_0+1$. We obtain estimates for the transition density of the continuous time simple random walk $Y$ on ${\\cal G}$; the process satisfies anomalous diffusion and has spectral dimension 4/3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-07T06:05:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60J80",
      "60J35"
    ],
    "keywords": [
      "incipient infinite cluster",
      "continuous time simple random walk",
      "process satisfies anomalous diffusion",
      "transition density",
      "spectral dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3118B"
    }
  }
}