{
  "id": "1005.5417",
  "version": "v2",
  "published": "2010-05-28T23:45:35.000Z",
  "updated": "2010-06-28T15:49:41.000Z",
  "title": "Recursions and tightness for the maximum of the discrete, two dimensional Gaussian Free Field",
  "authors": [
    "Erwin Bolthausen",
    "Jean-Dominique Deuschel",
    "Ofer Zeitouni"
  ],
  "comment": "Proof significantly shortened following a remark of Y. Peres",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the maximum of the discrete two dimensional Gaussian free field in a box, and prove the existence of a (dense) deterministic subsequence along which the maximum, centered at its mean, is tight; this still leaves open the conjecture that tightness holds without the need for subsequences. The method of proof relies on an argument developed by Dekking and Host for branching random walks with bounded increments and on comparison results specific to Gaussian fields.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-28T15:49:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60J80"
    ],
    "keywords": [
      "dimensional gaussian free field",
      "recursions",
      "comparison results specific",
      "gaussian fields",
      "deterministic subsequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.5417B"
    }
  }
}