{
  "id": "2501.03195",
  "version": "v1",
  "published": "2025-01-06T18:13:21.000Z",
  "updated": "2025-01-06T18:13:21.000Z",
  "title": "Parking on the Random Recursive Tree",
  "authors": [
    "Alice Contat",
    "Lucile Laulin"
  ],
  "comment": "15 pages, 5 figures; comments are welcome !",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We study the parking process on the random recursive tree. We first prove that although the random recursive tree has a non-degenerate Benjamini--Schramm limit, the phase transition for the parking process appears at density $0$. We then identify the critical window for appearance of a positive flux of cars with high probability. In the case of binary car arrivals, this happens at density $ \\log (n)^{-2+o(1)}$ where $n$ is the size of the tree. This is the first work that studies the parking process on trees with possibly large degree vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-06T18:13:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random recursive tree",
      "parking process",
      "non-degenerate benjamini-schramm limit",
      "binary car arrivals",
      "possibly large degree vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}