{
  "id": "1011.0299",
  "version": "v3",
  "published": "2010-11-01T12:03:13.000Z",
  "updated": "2011-10-14T11:44:42.000Z",
  "title": "Large Deviations for Random Matricial Moment Problems",
  "authors": [
    "Fabrice Gamboa",
    "Jan Nagel",
    "Alain Rouault",
    "Jens Wagener"
  ],
  "comment": "34 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the moment space $\\mathcal{M}_n^{K}$ corresponding to $p \\times p$ complex matrix measures defined on $K$ ($K=[0,1]$ or $K=\\D$). We endow this set with the uniform law. We are mainly interested in large deviations principles (LDP) when $n \\rightarrow \\infty$. First we fix an integer $k$ and study the vector of the first $k$ components of a random element of $\\mathcal{M}_n^{K}$. We obtain a LDP in the set of $k$-arrays of $p\\times p$ matrices. Then we lift a random element of $\\mathcal{M}_n^{K}$ into a random measure and prove a LDP at the level of random measures. We end with a LDP on Carth\\'eodory and Schur random functions. These last functions are well connected to the above random measure. In all these problems, we take advantage of the so-called canonical moments technique by introducing new (matricial) random variables that are independent and have explicit distributions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-10-14T11:44:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "60F10"
    ],
    "keywords": [
      "random matricial moment problems",
      "random measure",
      "random element",
      "large deviations principles",
      "schur random functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.0299G"
    }
  }
}