{
  "id": "1509.02251",
  "version": "v1",
  "published": "2015-09-08T04:21:05.000Z",
  "updated": "2015-09-08T04:21:05.000Z",
  "title": "Coupling and an application to level-set percolation of the Gaussian free field",
  "authors": [
    "Alain-Sol Sznitman"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a general enough set-up and obtain a refinement of the coupling between the Gaussian free field and random interlacements recently constructed by Titus Lupu in arXiv:1402.0298. We apply our results to level-set percolation of the Gaussian free field on a $(d+1)$-regular tree, when $d \\ge 2$, and derive bounds on the critical value $h_*$. In particular, we show that $0 < h_* < \\sqrt{2u_*}$, where $u_*$ denotes the critical level for the percolation of the vacant set of random interlacements on a $(d+1)$-regular tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-08T04:21:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60G15",
      "60J27",
      "60J80",
      "82B43"
    ],
    "keywords": [
      "gaussian free field",
      "level-set percolation",
      "regular tree",
      "random interlacements",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150902251S"
    }
  }
}