{
  "id": "1302.7024",
  "version": "v2",
  "published": "2013-02-27T23:07:42.000Z",
  "updated": "2014-03-26T22:41:35.000Z",
  "title": "Level set percolation for random interlacements and the Gaussian free field",
  "authors": [
    "Pierre-François Rodriguez"
  ],
  "comment": "32 pages, 1 figure",
  "journal": "Stoch. Proc. Appl. 124(4), 1469-1502 (2014)",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider continuous-time random interlacements on Z^d, d greater or equal to 3, and investigate the percolation model where a site x of Z^d is occupied if the total amount of time spent at x by all the trajectories of the interlacement at level u > 0 exceeds some given non-negative parameter, and empty otherwise. Thus, the set of occupied sites forms a subset of the interlacement at level u. We also investigate percolation properties of empty sites. A recent isomorphism theorem arXiv:1111.4818 of Sznitman enables us to \"translate\" some of the relevant questions into the language of level-set percolation for the Gaussian free field on Z^d, d greater or equal to 3, for which useful tools have been developed in arXiv:1202.5172. We also gain new insights of independent interest concerning \"two-sided\" level-set percolation, where a site x of Z^d is occupied if and only if the absolute value of the field variable at that site exceeds a given non-negative level.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-26T22:41:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G55",
      "60G60",
      "60K35",
      "82B43"
    ],
    "keywords": [
      "gaussian free field",
      "level set percolation",
      "level-set percolation",
      "continuous-time random interlacements",
      "percolation properties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.7024R"
    }
  }
}