{
  "id": "1308.6817",
  "version": "v3",
  "published": "2013-08-30T18:30:12.000Z",
  "updated": "2013-10-21T16:05:15.000Z",
  "title": "Determinantal point processes in the plane from products of random matrices",
  "authors": [
    "Kartick Adhikari",
    "Nanda Kishore Reddy",
    "Tulasi Ram Reddy",
    "Koushik Saha"
  ],
  "comment": "31 pages, 0 figure. Added a reference to the previous version",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of $k$ independent $n\\times n$ matrices with i.i.d. complex Gaussian entries with a few of matrices being inverted. In second example we calculate the same for (compatible) product of rectangular matrices with i.i.d. Gaussian entries and in last example we calculate for product of independent truncated unitary random matrices. We derive exact expressions for limiting expected empirical spectral distributions of above mentioned ensembles.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-21T16:05:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "60G55"
    ],
    "keywords": [
      "determinantal point processes",
      "expected empirical spectral distributions",
      "gaussian entries",
      "independent truncated unitary random matrices",
      "random matrix ensembles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016AnIHP..52...16A"
    }
  }
}