{
  "id": "0903.5450",
  "version": "v1",
  "published": "2009-03-31T13:03:04.000Z",
  "updated": "2009-03-31T13:03:04.000Z",
  "title": "On an average over the Gaussian Unitary Ensemble",
  "authors": [
    "F. Mezzadri",
    "M. Y. Mo"
  ],
  "comment": "28 pages, 3 figures",
  "journal": "Int. Math. Res. Notices (2009), Vol. 2009: article ID rnp062, 30 pages",
  "doi": "10.1093/imrn/rnp062",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble with weight exp(-z^2/2x^2 + t/x - x^2/2). We compute the leading order term of the partition function and of the coefficients of its Taylor expansion. Our results are valid in the range N^(-1/2) < z < N^(1/4). Such partition function contains all the information on a new statistics of the eigenvalues of matrices in the Gaussian Unitary Ensemble (GUE) that was introduced by Berry and Shukla (J. Phys. A: Math. Theor., Vol. 41 (2008), 385202, arXiv:0807.3474). It can also be interpreted as the moment generating function of a singular linear statistics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-31T13:03:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52",
      "35Q15"
    ],
    "keywords": [
      "gaussian unitary ensemble",
      "partition function contains",
      "large matrix dimension",
      "singular linear statistics",
      "asymptotic limit"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.5450M"
    }
  }
}