{
  "id": "1109.5109",
  "version": "v3",
  "published": "2011-09-23T15:21:04.000Z",
  "updated": "2013-07-26T11:10:37.000Z",
  "title": "Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $β=2$",
  "authors": [
    "Mario Kieburg"
  ],
  "comment": "23 pages; PACS: 02.10.Yn, 02.50.-r, 05.90.+m, 12.38.-t",
  "journal": "J. Phys. A: Math. Theor. 45 095205 (2012)",
  "doi": "10.1088/1751-8113/45/9/095205",
  "categories": [
    "math-ph",
    "hep-lat",
    "hep-th",
    "math.MP"
  ],
  "abstract": "In the past decades, determinants and Pfaffians were found for eigenvalue correlations of various random matrix ensembles. These structures simplify the average over a large number of ratios of characteristic polynomials to integrations over one and two characteristic polynomials only. Up to now it was thought that determinants occur for ensembles with Dyson index $\\beta=2$ whereas Pfaffians only for ensembles with $\\beta=1,4$. We derive a non-trivial Pfaffian determinant for $\\beta=2$ random matrix ensembles which is similar to the one for $\\beta=1,4$. Thus, it unveils a hidden universality of this structure. We also give a general relation between the orthogonal polynomials related to the determinantal structure and the skew-orthogonal polynomials corresponding to the Pfaffian. As a particular example we consider the chiral unitary ensembles in great detail.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-26T11:10:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "33C45",
      "42C05",
      "60B20",
      "05.90.+m",
      "02.10.Yn",
      "12.38.-t",
      "02.50.-r"
    ],
    "keywords": [
      "random matrix theory",
      "surprising pfaffian factorizations",
      "dyson index",
      "random matrix ensembles",
      "characteristic polynomials"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2012,
      "month": "Mar",
      "volume": 45,
      "number": 9,
      "pages": "095205"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 928319,
      "adsabs": "2012JPhA...45i5205K"
    }
  }
}