{
  "id": "1510.07604",
  "version": "v1",
  "published": "2015-10-26T19:27:06.000Z",
  "updated": "2015-10-26T19:27:06.000Z",
  "title": "Finite range decomposition for a general class of elliptic operators",
  "authors": [
    "Eris Runa"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We consider a family of gradient Gaussian vector fields on $\\Z^d$, where the covariance operator is not translation invariant. A uniform finite range decomposition of the corresponding covariance operators is proven, i.e., the covariance operator can be written as a sum of covariance operators whose kernels are supported within cubes of increasing diameter. An optimal regularity bound for the subcovariance operators is proven. We also obtain regularity bounds as we vary the coefficients defining the gradient Gaussian measures. This extends a result of S. Adams, R. Koteck\\'y and S. M\\\"uller \\cite{1202.1158}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-26T19:27:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general class",
      "elliptic operators",
      "gradient gaussian vector fields",
      "uniform finite range decomposition",
      "optimal regularity bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151007604R"
    }
  }
}