{
  "id": "0812.2669",
  "version": "v4",
  "published": "2008-12-14T19:23:40.000Z",
  "updated": "2009-12-30T21:42:19.000Z",
  "title": "Heat-kernel estimates for random walk among random conductances with heavy tail",
  "authors": [
    "Omar Boukhadra"
  ],
  "comment": "Version to appear in SPA",
  "journal": "Stochastic Processes and their Applications 120 (2010) 182-194",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study models of discrete-time, symmetric, $\\Z^{d}$-valued random walks in random environments, driven by a field of i.i.d. random nearest-neighbor conductances $\\omega_{xy}\\in[0,1]$, with polynomial tail near 0 with exponent $\\gamma>0$. We first prove for all $d\\geq5$ that the return probability shows an anomalous decay (non-Gaussian) that approches (up to sub-polynomial terms) a random constant times $n^{-2}$ when we push the power $\\gamma$ to zero. In contrast, we prove that the heat-kernel decay is as close as we want, in a logarithmic sense, to the standard decay $n^{-d/2}$ for large values of the parameter $\\gamma$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-12-30T21:42:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60J10",
      "60K37"
    ],
    "keywords": [
      "random conductances",
      "heat-kernel estimates",
      "heavy tail",
      "random nearest-neighbor conductances",
      "random constant times"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.2669B"
    }
  }
}