{
  "id": "1105.3929",
  "version": "v3",
  "published": "2011-05-19T16:42:10.000Z",
  "updated": "2011-06-26T10:03:30.000Z",
  "title": "Zeroes of Gaussian Analytic Functions with Translation-Invariant Distribution",
  "authors": [
    "Naomi Feldheim"
  ],
  "comment": "24 pages, 1 figure. Some corrections were made and presentation was improved",
  "doi": "10.1007/s11856-012-0130-0",
  "categories": [
    "math.PR",
    "math-ph",
    "math.CV",
    "math.MP"
  ],
  "abstract": "We study zeroes of Gaussian analytic functions in a strip in the complex plane, with translation-invariant distribution. We prove that the a limiting horizontal mean counting-measure of the zeroes exists almost surely, and that it is non-random if and only if the spectral measure is continuous (or degenerate). In this case, the mean zero-counting measure is computed in terms of the spectral measure. We compare the behavior with Gaussian analytic function with symmetry around the real axis. These results extend a work by Norbert Wiener.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-06-26T10:03:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian analytic function",
      "translation-invariant distribution",
      "spectral measure",
      "limiting horizontal mean counting-measure",
      "study zeroes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.3929F"
    }
  }
}