{
  "id": "1501.05506",
  "version": "v1",
  "published": "2015-01-22T14:23:51.000Z",
  "updated": "2015-01-22T14:23:51.000Z",
  "title": "Transformations of polynomial ensembles",
  "authors": [
    "Arno B. J. Kuijlaars"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A polynomial ensemble is a probability density function for the position of $n$ real particles of the form $\\frac{1}{Z_n} \\, \\prod_{j<k} (x_k-x_j) \\, \\det \\left[ f_k (x_j) \\right]_{j,k=1}^n$, for certain functions $f_1, \\ldots, f_n$. Such ensembles appear frequently as the joint eigenvalue density of random matrices. We present a number of transformations that preserve the structure of a polynomial ensemble. These transformations include the restriction of a Hermitian matrix by removing one row and one column, a rank-one modification of a Hermitian matrix, and the extension of a Hermitian matrix by adding an extra row and column with complex Gaussians. A special case of the latter result gives an elementary approach to the joint eigenvalue density of a GUE matrix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-22T14:23:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial ensemble",
      "joint eigenvalue density",
      "hermitian matrix",
      "transformations",
      "probability density function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150105506K"
    }
  }
}