{
  "id": "1009.4677",
  "version": "v2",
  "published": "2010-09-23T18:31:26.000Z",
  "updated": "2011-08-12T21:53:36.000Z",
  "title": "Smallest eigenvalue distributions for two classes of $β$-Jacobi ensembles",
  "authors": [
    "Ioana Dumitriu"
  ],
  "comment": "15 pages, 6 figures",
  "categories": [
    "math.PR",
    "cs.DC",
    "cs.NA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We compute the exact and limiting smallest eigenvalue distributions for two classes of $\\beta$-Jacobi ensembles not covered by previous studies. In the general $\\beta$ case, these distributions are given by multivariate hypergeometric ${}_2F_{1}^{2/\\beta}$ functions, whose behavior can be analyzed asymptotically for special values of $\\beta$ which include $\\beta \\in 2\\mathbb{N}_{+}$ as well as for $\\beta = 1$. Interest in these objects stems from their connections (in the $\\beta = 1,2$ cases) to principal submatrices of Haar-distributed (orthogonal, unitary) matrices appearing in randomized, communication-optimal, fast, and stable algorithms for eigenvalue computations \\cite{DDH07}, \\cite{BDD10}.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-08-12T21:53:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "15B52"
    ],
    "keywords": [
      "jacobi ensembles",
      "limiting smallest eigenvalue distributions",
      "multivariate hypergeometric",
      "eigenvalue computations",
      "special values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.4677D"
    }
  }
}