{
  "id": "1107.4135",
  "version": "v1",
  "published": "2011-07-20T22:45:00.000Z",
  "updated": "2011-07-20T22:45:00.000Z",
  "title": "Universality of Correlations for Random Analytic Functions",
  "authors": [
    "Shannon Starr"
  ],
  "comment": "10 pages, 3 figures. To appear in Contemporary Mathematics, proceedings of the Arizona School of Analysis with Applications, March 2010",
  "categories": [
    "math.PR"
  ],
  "abstract": "We review a result obtained with Andrew Ledoan and Marco Merkli. Consider a random analytic function $f(z) = \\sum_{n=0}^{\\infty} a_n X_n z^n$, where the $X_n$'s are i.i.d., complex valued random variables with mean zero and unit variance, and the coefficients $a_n$ are non-random and chosen so that the variance transforms covariantly under conformal transformations of the domain. If the $X_n$'s are Gaussian, this is called a Gaussian analytic function (GAF). We prove that, even if the coefficients are not Gaussian, the zero set converges in distribution to that of a GAF near the boundary of the domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-20T22:45:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30B20",
      "60B12",
      "60G15"
    ],
    "keywords": [
      "random analytic function",
      "universality",
      "correlations",
      "gaussian analytic function",
      "zero set converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.4135S"
    }
  }
}