{
  "id": "1402.1648",
  "version": "v1",
  "published": "2014-02-07T14:19:53.000Z",
  "updated": "2014-02-07T14:19:53.000Z",
  "title": "Spectral Expansions of Homogeneous and Isotropic Tensor-Valued Random Fields",
  "authors": [
    "Anatoliy Malyarenko",
    "Martin Ostoja-Starzewski"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We establish spectral expansions of homogeneous and isotropic random fields taking values in the $3$-dimensional Euclidean space $E^3$ and in the space $\\mathsf{S}^2(E^3)$ of symmetric rank $2$ tensors over $E^3$. The former is a model of turbulent fluid velocity, while the latter is a model for the random stress tensor or the random conductivity tensor. We found a link between the theory of random fields and the theory of finite-dimensional convex compacta.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-07T14:19:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G60"
    ],
    "keywords": [
      "isotropic tensor-valued random fields",
      "isotropic random fields",
      "finite-dimensional convex compacta",
      "dimensional euclidean space",
      "homogeneous"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.1648M"
    }
  }
}