{
  "id": "1409.0801",
  "version": "v1",
  "published": "2014-09-02T17:33:53.000Z",
  "updated": "2014-09-02T17:33:53.000Z",
  "title": "Quantitative results on the corrector equation in stochastic homogenization",
  "authors": [
    "Antoine Gloria",
    "Felix Otto"
  ],
  "comment": "57 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We derive optimal estimates in stochastic homogenization of linear elliptic equations in divergence form in dimensions $d\\ge 2$. In previous works we studied the model problem of a discrete elliptic equation on $\\mathbb{Z}^d$. Under the assumption that a spectral gap estimate holds in probability, we proved that there exists a stationary corrector field in dimensions $d>2$ and that the energy density of that corrector behaves as if it had finite range of correlation in terms of the variance of spatial averages - the latter decays at the rate of the central limit theorem. In this article we extend these results, and several other estimates, to the case of a continuum linear elliptic equation whose (not necessarily symmetric) coefficient field satisfies a continuum version of the spectral gap estimate. In particular, our results cover the example of Poisson random inclusions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-02T17:33:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27",
      "39A70",
      "60H25",
      "60F99"
    ],
    "keywords": [
      "stochastic homogenization",
      "corrector equation",
      "quantitative results",
      "spectral gap estimate holds",
      "continuum linear elliptic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.0801G"
    }
  }
}