{
  "id": "1207.0125",
  "version": "v2",
  "published": "2012-06-30T19:03:30.000Z",
  "updated": "2012-10-19T19:32:37.000Z",
  "title": "On the Distribution of Critical Points of a Polynomial",
  "authors": [
    "Sneha Dey Subramanian"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper proves that if points $Z_1,Z_2,...$ are chosen independently and identically using some measure $\\mu$ from the unit circle in the complex plane, with $p_n(z) = (z-Z_1)(z-Z_2)...(z-Z_n)$, then the empirical distribution of the critical points of $p_n$ converges weakly to $\\mu$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-19T19:32:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical points",
      "polynomial",
      "unit circle",
      "complex plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.0125D"
    }
  }
}