{
  "id": "1510.08290",
  "version": "v1",
  "published": "2015-10-28T12:46:57.000Z",
  "updated": "2015-10-28T12:46:57.000Z",
  "title": "The corrector in stochastic homogenization: Near-optimal rates with optimal stochastic integrability",
  "authors": [
    "Antoine Gloria",
    "Felix Otto"
  ],
  "comment": "55 pages",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We consider uniformly elliptic coefficient fields that are randomly distributed according to a stationary ensemble of a finite range of dependence. We show that the gradient $\\nabla\\phi$ of the corrector $\\phi$, when spatially averaged over a scale $R\\gg 1$ decays like $R^{-\\alpha}$ for any $\\alpha<\\frac{d}{2}$. We establish these rates on the level of Gaussian bounds in terms of the stochastic integrability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-28T12:46:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J15",
      "35K10",
      "35B27",
      "60H25",
      "60F99"
    ],
    "keywords": [
      "optimal stochastic integrability",
      "near-optimal rates",
      "stochastic homogenization",
      "uniformly elliptic coefficient fields",
      "finite range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151008290G"
    }
  }
}