{
  "id": "1102.3517",
  "version": "v1",
  "published": "2011-02-17T07:52:41.000Z",
  "updated": "2011-02-17T07:52:41.000Z",
  "title": "On distribution of zeros of random polynomials in complex plane",
  "authors": [
    "Ildar Ibragimov",
    "Dmitry Zaporozhets"
  ],
  "categories": [
    "math.PR",
    "math.CV"
  ],
  "abstract": "Let $G_n(z)=\\xi_0+\\xi_1z+...+\\xi_n z^n$ be a random polynomial with i.i.d. coefficients (real or complex). We show that the arguments of the roots of $G_n(z)$ are uniformly distributed in $[0,2\\pi]$ asymptotically as $n\\to\\infty$. We also prove that the condition $\\E\\ln(1+|\\xi_0|)<\\infty$ is necessary and sufficient for the roots to asymptotically concentrate near the unit circumference.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-17T07:52:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26C10"
    ],
    "keywords": [
      "random polynomial",
      "complex plane",
      "distribution",
      "unit circumference"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.3517I"
    }
  }
}