{
  "id": "1407.0269",
  "version": "v3",
  "published": "2014-07-01T14:58:34.000Z",
  "updated": "2015-10-29T12:08:44.000Z",
  "title": "Disconnection and level-set percolation for the Gaussian free field",
  "authors": [
    "Alain-Sol Sznitman"
  ],
  "comment": "40 pages, has appeared in the special issue of the J. Math. Soc. Japan on the centennial of the birth of Kiyosi Ito",
  "journal": "J. Math. Soc. Japan, 67(4), 1801-1843, 2015",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the level-set percolation of the Gaussian free field on Z^d, d bigger or equal to 3. We consider a level alpha such that the excursion-set of the Gaussian free field above alpha percolates. We derive large deviation estimates on the probability that the excursion-set of the Gaussian free field below the level alpha disconnects a box of large side-length from the boundary of a larger homothetic box. It remains an open question whether our asymptotic upper and lower bounds are matching. With the help of a recent work of Lupu, see arXiv:1402.0298, we are able to infer some asymptotic upper bounds for similar disconnection problems by random interlacements, or by simple random walk.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-11T12:45:02.000Z",
      "comment": "40 pages, some typos corrected and comments added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-10-29T12:08:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60K35",
      "60G15",
      "82B43"
    ],
    "keywords": [
      "gaussian free field",
      "level-set percolation",
      "level alpha disconnects",
      "simple random walk",
      "larger homothetic box"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.0269S"
    }
  }
}