{
  "annotation_id": "81971f6d-916c-46cd-b041-6a0322b6566d",
  "date_created": "2026-02-17T05:53:15.714000Z",
  "date_modified": "2026-02-17T05:53:15.714000Z",
  "file_hash": "c20ed0d1459027845b7a7c19236576246f2b2168650dd7ba7bc694200b65c74d",
  "private": false,
  "record": {
    "abstract": "Consider $M_n$ the maximal position at generation $n$ of a supercritical branching random walk. A\\\"id\\\u0027ekon (2013) obtained and described the convergence in law, as time $n$ goes to infinity, of $M_n-m_n$, where $m_n$ is an explicit function. Equivalently, he identified the limit of $\\mathbb{P}(M_n \u003e m_n + x)$, for any $x \\in \\mathbb{R}$. More recently, Luo (2025) gave an asymptotic equivalent for the upper large deviation probability, that is $\\mathbb{P}(M_n \u003e m_n + xn)$, for $x \u003e 0$. In this work, we study an intermediate regime, called upper moderate deviation. We obtain, under close-to-optimal integrability conditions, an asymptotic equivalent for $\\mathbb{P}(M_n \u003e m_n + x_n)$, where $x_n$ is such that $x_n \\to \\infty$ and $x_n = O(\\sqrt{n})$. Our proof is based on a strategy due to Bramson, Ding, and Zeitouni (2016). As a byproduct, we obtain information about the typical behavior of particles contributing to such deviations. Finally, we apply our main result to show the convergence in law of the centered maximum of a two-speed branching random walk in the mean regime and describe its limit.",
    "arxiv_id": "2601.08766",
    "authors": [
      "Louis Chataignier",
      "Lianghui Luo"
    ],
    "categories": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Upper moderate deviation probabilities for the maximum of a branching random walk",
    "url": "https://arxiv.org/abs/2601.08766",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "27a242d5-f8df-4860-a2da-8d854b1b3cfe",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}