{
  "id": "math-ph/0608052",
  "version": "v1",
  "published": "2006-08-23T03:33:08.000Z",
  "updated": "2006-08-23T03:33:08.000Z",
  "title": "A note on biorthogonal ensembles",
  "authors": [
    "Patrick Desrosiers",
    "Peter J. Forrester"
  ],
  "comment": "20 pages",
  "journal": "Journal of Approximation Theory 152 (2008) 167--187",
  "doi": "10.1016/j.jat.2007.08.006",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider ensembles of random matrices, known as biorthogonal ensembles, whose eigenvalue probability density function can be written as a product of two determinants. These systems are closely related to multiple orthogonal functions. It is known that the eigenvalue correlation functions of such ensembles can be written as a determinant of a kernel function. We show that the kernel is itself an average of a single ratio of characteristic polynomials. In the same vein, we prove that the type I multiple polynomials can be expressed as an average of the inverse of a characteristic polynomial. We finally introduce a new biorthogonal matrix ensemble, namely the chiral unitary perturbed by a source term.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-08-23T03:33:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52",
      "33C47"
    ],
    "keywords": [
      "biorthogonal ensembles",
      "eigenvalue probability density function",
      "characteristic polynomial",
      "multiple orthogonal functions",
      "eigenvalue correlation functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.ph...8052D"
    }
  }
}