{
  "id": "1402.1924",
  "version": "v2",
  "published": "2014-02-09T07:37:43.000Z",
  "updated": "2015-02-15T08:58:33.000Z",
  "title": "Correlation structure of the corrector in stochastic homogenization",
  "authors": [
    "Jean-Christophe Mourrat",
    "Felix Otto"
  ],
  "comment": "21 pages. V2: minor modifications",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "Recently, the quantification of errors in the stochastic homogenization of divergence-form operators has witnessed important progress. Our aim now is to go beyond error bounds, and give precise descriptions of the effect of the randomness, in the large-scale limit. This paper is a first step in this direction. Our main result is to identify the correlation structure of the corrector, in dimension 3 and higher. This correlation structure is similar to, but different from that of a Gaussian free field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-09T07:37:43.000Z",
      "comment": "21 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-15T08:58:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27",
      "35J15",
      "35R60",
      "82D30"
    ],
    "keywords": [
      "correlation structure",
      "stochastic homogenization",
      "gaussian free field",
      "error bounds",
      "precise descriptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.1924M"
    }
  }
}