{
  "id": "hep-th/9304063",
  "version": "v2",
  "published": "1993-04-16T06:02:51.000Z",
  "updated": "1999-01-29T23:00:56.000Z",
  "title": "Level-Spacing Distributions and the Bessel Kernel",
  "authors": [
    "Craig A. Tracy",
    "Harold Widom"
  ],
  "comment": "18 pages, resubmitted to make postscript compatible, no changes to manuscript content",
  "journal": "Commun.Math.Phys. 161 (1994) 289-310",
  "doi": "10.1007/BF02099779",
  "categories": [
    "hep-th",
    "math-ph",
    "math.MP",
    "nlin.SI",
    "solv-int"
  ],
  "abstract": "The level spacing distributions which arise when one rescales the Laguerre or Jacobi ensembles of hermitian matrices is studied. These distributions are expressible in terms of a Fredholm determinant of an integral operator whose kernel is expressible in terms of Bessel functions of order $\\alpha$. We derive a system of partial differential equations associated with the logarithmic derivative of this Fredholm determinant when the underlying domain is a union of intervals. In the case of a single interval this Fredholm determinant is a Painleve tau function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1999-01-29T23:00:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bessel kernel",
      "level-spacing distributions",
      "fredholm determinant",
      "painleve tau function",
      "bessel functions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 34705
    }
  }
}