{
  "id": "1602.08428",
  "version": "v1",
  "published": "2016-02-26T18:35:47.000Z",
  "updated": "2016-02-26T18:35:47.000Z",
  "title": "Quenched invariance principles for the random conductance model on a random graph with degenerate ergodic weights",
  "authors": [
    "Jean-Dominique Deuschel",
    "Tuan Anh Nguyen",
    "Martin Slowik"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We consider a stationary and ergodic random field $\\{\\omega(e) : e \\in E_d\\}$ that is parameterized by the edge set of the Euclidean lattice $\\mathbb{Z}^d$, $d \\geq 2$. The random variable $\\omega(e)$, taking values in $[0, \\infty)$ and satisfying certain moment bounds, is thought of as the conductance of the edge $e$. Assuming that the set of edges with positive conductances give rise to a unique infinite cluster $\\mathcal{C}_{\\infty}(\\omega)$, we prove a quenched invariance principle for the continuous-time random walk among random conductances under certain moment conditions. An essential ingredient of our proof is a new anchored relative isoperimetric inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-26T18:35:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60F17",
      "82C41",
      "82B43"
    ],
    "keywords": [
      "quenched invariance principle",
      "random conductance model",
      "degenerate ergodic weights",
      "random graph",
      "unique infinite cluster"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160208428D"
    }
  }
}