{
  "id": "2207.03016",
  "version": "v1",
  "published": "2022-07-06T23:38:43.000Z",
  "updated": "2022-07-06T23:38:43.000Z",
  "title": "Maximum of Branching Brownian Motion among mild obstacles",
  "authors": [
    "Lisa Hartung",
    "Michèle Lehnen"
  ],
  "comment": "36 pages, 4 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the height of the maximal particle at time $t$ of a one dimensional branching Brownian motion with a space-dependent branching rate. The branching rate is set to zero in finitely many intervals (obstacles) of order $t$. We obtain almost sure asymptotics of the first order of the maximum, describe the path of a particle reaching this height and describe its dependence on the size and location of the obstacles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-06T23:38:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mild obstacles",
      "dimensional branching brownian motion",
      "sure asymptotics",
      "maximal particle",
      "first order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}