{
  "id": "2409.02479",
  "version": "v1",
  "published": "2024-09-04T07:07:23.000Z",
  "updated": "2024-09-04T07:07:23.000Z",
  "title": "An ergodic theorem for the maximum of branching Brownian motion with absorption",
  "authors": [
    "Fan Yang"
  ],
  "comment": "14 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study branching Brownian motion with absorption, in which particles undergo Brownian motions and are killed upon hitting the absorption barrier. We prove that the empirical distribution function of the maximum of this process converges almost surely to a randomly shifted Gumbel distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-04T07:07:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60G70"
    ],
    "keywords": [
      "ergodic theorem",
      "particles undergo brownian motions",
      "study branching brownian motion",
      "process converges",
      "randomly shifted gumbel distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}