{
  "id": "1409.4213",
  "version": "v1",
  "published": "2014-09-15T11:35:26.000Z",
  "updated": "2014-09-15T11:35:26.000Z",
  "title": "A central limit theorem for random walks on the dual of a compact Grassmannian",
  "authors": [
    "Margit Rösler",
    "Michael Voit"
  ],
  "categories": [
    "math.CA",
    "math.PR",
    "math.RT"
  ],
  "abstract": "We consider compact Grassmann manifolds G/K over the real, complex or quaternionic numbers whose spherical functions are Heckman-Opdam polynomials of type BC. From an explicit integral representation of these polynomials we deduce a sharp Mehler-Heine formula, that is an approximation of the Heckman-Opdam polynomials in terms of Bessel functions, with a precise estimate on the error term. This result is used to derive a central limit theorem for random walks on the semi-lattice parametrizing the dual of G/K, which are constructed by successive decompositions of tensor powers of spherical representations of G. The limit is the distribution of a Laguerre ensemble in random matrix theory. Most results of this paper are established for a larger continuous set of multiplicity parameters beyond the group cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-15T11:35:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C52",
      "43A90",
      "60F05",
      "60B15",
      "43A62",
      "33C80",
      "33C67"
    ],
    "keywords": [
      "central limit theorem",
      "random walks",
      "compact grassmannian",
      "heckman-opdam polynomials",
      "compact grassmann manifolds g/k"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.4213R"
    }
  }
}