{
  "id": "2311.13441",
  "version": "v1",
  "published": "2023-11-22T15:07:31.000Z",
  "updated": "2023-11-22T15:07:31.000Z",
  "title": "On convergence of points to limiting processes, with an application to zeta zeros",
  "authors": [
    "Juan Arias de Reyna",
    "Brad Rodgers"
  ],
  "comment": "29 pages, comments welcome",
  "categories": [
    "math.NT",
    "math.PR"
  ],
  "abstract": "This paper considers sequences of points on the real line which have been randomly translated, and provides conditions under which various notions of convergence to a limiting point process are equivalent. In particular we consider convergence in correlation, convergence in distribution, and convergence of spacings between points. We also prove a simple Tauberian theorem regarding rescaled correlations. The results are applied to zeros of the Riemann zeta-function to show that several ways to state the GUE Hypothesis are equivalent. The proof relies on a moment bound of A. Fujii.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-22T15:07:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convergence",
      "zeta zeros",
      "limiting processes",
      "application",
      "tauberian theorem regarding rescaled correlations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}