{
  "id": "1412.4703",
  "version": "v1",
  "published": "2014-12-15T17:59:34.000Z",
  "updated": "2014-12-15T17:59:34.000Z",
  "title": "Critical points of random polynomials and characteristic polynomials of random matrices",
  "authors": [
    "Sean O'Rourke"
  ],
  "comment": "28 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $p_n$ be the characteristic polynomial of an $n \\times n$ random matrix drawn from one of the compact classical matrix groups. We show that the critical points of $p_n$ converge to the uniform distribution on the unit circle as $n$ tends to infinity. More generally, we show the same limit for a class of random polynomials whose roots lie on the unit circle. Our results extend the work of Pemantle-Rivin and Kabluchko to the setting where the roots are neither independent nor identically distributed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-15T17:59:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characteristic polynomial",
      "random polynomials",
      "critical points",
      "random matrices",
      "unit circle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.4703O"
    }
  }
}