{
  "id": "1703.08163",
  "version": "v1",
  "published": "2017-03-23T17:50:02.000Z",
  "updated": "2017-03-23T17:50:02.000Z",
  "title": "On the asymptotic variance of the number of real roots of random polynomial systems",
  "authors": [
    "Diego Armentano",
    "Jean-Marc Azaïs",
    "Federico Dalmao",
    "José R. León"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We obtain the asymptotic variance, as the degree goes to infinity, of the normalized number of real roots of a square Kostlan-Shub-Smale random polynomial system of any size. Our main tools are the Kac-Rice formula for the second factorial moment of the number of roots and a Hermite expansion of this random variable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-23T17:50:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "30C15",
      "60G60",
      "65H10"
    ],
    "keywords": [
      "asymptotic variance",
      "real roots",
      "square kostlan-shub-smale random polynomial system",
      "second factorial moment",
      "main tools"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}