{
  "id": "1505.06069",
  "version": "v1",
  "published": "2015-05-22T13:33:42.000Z",
  "updated": "2015-05-22T13:33:42.000Z",
  "title": "Homogenization via sprinkling",
  "authors": [
    "Itai Benjamini",
    "Vincent Tassion"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that a superposition of an $\\varepsilon$-Bernoulli bond percolation and any everywhere percolating subgraph of $\\mathbb Z^d$, $d\\ge 2$, results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli percolation. This result, which confirms a conjecture of the first author together with H\\\"aggstr\\\"om and Schramm (2000), is mainly motivated by obtaining finite volume characterizations of uniqueness for general percolation processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-22T13:33:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "05C80"
    ],
    "keywords": [
      "homogenization",
      "renormalization dominates supercritical bernoulli percolation",
      "bernoulli bond percolation",
      "obtaining finite volume characterizations",
      "general percolation processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150506069B"
    }
  }
}