{
  "id": "2505.10137",
  "version": "v1",
  "published": "2025-05-15T10:11:33.000Z",
  "updated": "2025-05-15T10:11:33.000Z",
  "title": "Small deviations for critical Galton-Watson processes with infinite variance",
  "authors": [
    "Vladimir Vatutin",
    "Elena Dyakonova",
    "Yakubdjan Khusanbaev"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the asymptotic behavior of small deviation probabilities for the critical Galton-Watson processes with infinite variance of the offspring sizes of particles and apply the obtained result to investigate the structure of a reduced critical Galton-Watson process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-15T10:11:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60F10"
    ],
    "keywords": [
      "infinite variance",
      "small deviation probabilities",
      "asymptotic behavior",
      "reduced critical galton-watson process",
      "offspring sizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}