{
  "id": "2308.16447",
  "version": "v1",
  "published": "2023-08-31T04:26:43.000Z",
  "updated": "2023-08-31T04:26:43.000Z",
  "title": "Non-simple systoles on random hyperbolic surfaces for large genus",
  "authors": [
    "Yuxin He",
    "Yang Shen",
    "Yunhui Wu",
    "Yuhao Xue"
  ],
  "comment": "47 pages, 11 figures. Comments welcome",
  "categories": [
    "math.GT",
    "math.CV",
    "math.DG",
    "math.PR"
  ],
  "abstract": "In this paper, we investigate the asymptotic behavior of the non-simple systole, which is the length of a shortest non-simple closed geodesic, on a random closed hyperbolic surface on the moduli space $\\mathcal{M}_g$ of Riemann surfaces of genus $g$ endowed with the Weil-Petersson measure. We show that as the genus $g$ goes to infinity, the non-simple systole of a generic hyperbolic surface in $\\mathcal{M}_g$ behaves exactly like $\\log g$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-31T04:26:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random hyperbolic surfaces",
      "non-simple systole",
      "large genus",
      "generic hyperbolic surface",
      "shortest non-simple closed geodesic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}