{
  "id": "2505.07120",
  "version": "v1",
  "published": "2025-05-11T21:07:13.000Z",
  "updated": "2025-05-11T21:07:13.000Z",
  "title": "Asymptotic Mass Distribution of Random Holomorphic Sections",
  "authors": [
    "Turgay Bayraktar",
    "Afrim Bojnik"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CV",
    "math.DG",
    "math.PR"
  ],
  "abstract": "In this note, we prove a central limit theorem for the mass distribution of random holomorphic sections associated with a sequence of positive line bundles endowed with $\\mathscr{C}^3$ Hermitian metrics over a compact K\\\"{a}hler manifold. In addition, we show that almost every sequence of such random holomorphic sections exhibits quantum ergodicity in the sense of Zelditch.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-11T21:07:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random holomorphic sections",
      "asymptotic mass distribution",
      "central limit theorem",
      "positive line bundles",
      "hermitian metrics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}