{
  "id": "1606.02411",
  "version": "v1",
  "published": "2016-06-08T06:21:57.000Z",
  "updated": "2016-06-08T06:21:57.000Z",
  "title": "Level-set percolation for the Gaussian free field on a transient tree",
  "authors": [
    "Angelo Abächerli",
    "Alain-Sol Sznitman"
  ],
  "comment": "35 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate level-set percolation of the Gaussian free field on transient trees, for instance on super-critical Galton-Watson trees conditioned on non-extinction. Recently developed Dynkin-type isomorphism theorems provide a comparison with percolation of the vacant set of random interlacements, which is more tractable in the case of trees. If $h_*$ and $u_*$ denote the respective (non-negative) critical values of level-set percolation of the Gaussian free field and of the vacant set of random interlacements, we show here that $h_* < \\sqrt{2u}_*$ in a broad enough set-up, but provide an example where $0 = h_* = u_*$ occurs. We also obtain some sufficient conditions ensuring that $h_* > 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-08T06:21:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60G15",
      "60J10",
      "60J80",
      "82B43"
    ],
    "keywords": [
      "gaussian free field",
      "level-set percolation",
      "transient tree",
      "random interlacements",
      "vacant set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}