{
  "id": "0906.5223",
  "version": "v2",
  "published": "2009-06-29T08:48:29.000Z",
  "updated": "2009-09-10T12:33:13.000Z",
  "title": "Derivation of an eigenvalue probability density function relating to the Poincare disk",
  "authors": [
    "Peter J. Forrester",
    "Manjunath Krishnapur"
  ],
  "comment": "11 pages; To appear in J.Phys A",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "A result of Zyczkowski and Sommers [J.Phys.A, 33, 2045--2057 (2000)] gives the eigenvalue probability density function for the top N x N sub-block of a Haar distributed matrix from U(N+n). In the case n \\ge N, we rederive this result, starting from knowledge of the distribution of the sub-blocks, introducing the Schur decomposition, and integrating over all variables except the eigenvalues. The integration is done by identifying a recursive structure which reduces the dimension. This approach is inspired by an analogous approach which has been recently applied to determine the eigenvalue probability density function for random matrices A^{-1} B, where A and B are random matrices with entries standard complex normals. We relate the eigenvalue distribution of the sub-blocks to a many body quantum state, and to the one-component plasma, on the pseudosphere.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-10T12:33:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B23",
      "15A52"
    ],
    "keywords": [
      "eigenvalue probability density function relating",
      "poincare disk",
      "derivation",
      "entries standard complex normals",
      "random matrices"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/42/38/385204",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2009,
      "month": "Sep",
      "volume": 42,
      "number": 38,
      "pages": 385204
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JPhA...42L5204F"
    }
  }
}