{
  "id": "0706.0359",
  "version": "v1",
  "published": "2007-06-04T01:10:12.000Z",
  "updated": "2007-06-04T01:10:12.000Z",
  "title": "Boundary Conditions for Scaled Random Matrix Ensembles in the Bulk of the Spectrum",
  "authors": [
    "A. V. Kitaev",
    "N. S. Witte"
  ],
  "comment": "23 pages, 2 figures, to appear in proceedings of Symmetries and Integrability of Difference Equations VII, Melbourne 2006",
  "doi": "10.1088/1751-8113/40/42/S16",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A spectral average which generalises the local spacing distribution of the eigenvalues of random $ N\\times N $ hermitian matrices in the bulk of their spectrum as $ N\\to\\infty $ is known to be a $\\tau$-function of the fifth Painlev\\'e system. This $\\tau$-function, $ \\tau(s) $, has generic parameters and is transcendental but is characterised by particular boundary conditions about the singular point $s=0$, which we determine here. When the average reduces to the local spacing distribution we find that $\\tau$-function is of the separatrix, or partially truncated type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-04T01:10:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E35",
      "39A05",
      "37F10",
      "33C45",
      "34M55"
    ],
    "keywords": [
      "scaled random matrix ensembles",
      "boundary conditions",
      "local spacing distribution",
      "fifth painleve system",
      "average reduces"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2007,
      "month": "Oct",
      "volume": 40,
      "number": 42,
      "pages": 12725
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007JPhA...4012725K"
    }
  }
}