{
  "annotation_id": "890dbf74-6b4b-48d5-842c-4665c56b2867",
  "date_created": "2026-02-17T05:53:11.272000Z",
  "date_modified": "2026-02-17T05:53:11.272000Z",
  "file_hash": "37a6672e058e51ca0ef55166cbe403d2d877845a96b27e641a3787226f2fa0b3",
  "private": false,
  "record": {
    "abstract": "This work extends the studies on the minimum and extremal process of a supercritical branching random walk outside the boundary case which cannot be reduced to the boundary case. We study here the situation where the log-generating function explodes at $1$ and the random walk associated to the spine possesses a stretched exponential tail with exponent $b\\in(0,\\frac12)$. Under suitable conditions, we confirm the conjecture of Barral, Hu and Madaule [Bernoulli 24(2) 2018 801-841], and obtain the weak convergence for the minimum and the extremal process. We also establish an a.s. infimum result over all infinity rays of this system.",
    "arxiv_id": "2601.07129",
    "authors": [
      "Xinxin Chen",
      "Haojie Hou"
    ],
    "categories": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Minimum and extremal process for a branching random walk outside the boundary case",
    "url": "https://arxiv.org/abs/2601.07129",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e9c25933-6414-4e9a-ad7d-0e595304fbd0",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}