{
  "id": "1109.4659",
  "version": "v1",
  "published": "2011-09-21T21:50:00.000Z",
  "updated": "2011-09-21T21:50:00.000Z",
  "title": "Selberg Integrals, Super hypergeometric functions and Applications to $β$-Ensembles of Random Matrices",
  "authors": [
    "Patrick Desrosiers",
    "Dang-Zheng Liu"
  ],
  "comment": "43 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study a new Selberg-type integral with $n+m$ indeterminates, which turns out to be related to the deformed Calogero-Sutherland systems. We show that the integral satisfies a holonomic system of $n+m$ non-symmetric linear partial differential equations. We also prove that a particular hypergeometric function defined in terms of super Jack polynomials is the unique solution of the system. Some properties such as duality relations, integral formulas, Pfaff-Euler and Kummer transformations are also established. As a direct application, we evaluate the expectation value of ratios of characteristic polynomials in the classical $\\beta$-ensembles of Random Matrix Theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-21T21:50:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "05E05",
      "33C70"
    ],
    "keywords": [
      "super hypergeometric functions",
      "random matrices",
      "selberg integrals",
      "application",
      "non-symmetric linear partial differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.4659D"
    }
  }
}