{
  "id": "2408.01555",
  "version": "v1",
  "published": "2024-08-02T20:05:19.000Z",
  "updated": "2024-08-02T20:05:19.000Z",
  "title": "Tightness for branching random walk in a space-inhomogeneous random environment",
  "authors": [
    "Xaver Kriechbaum"
  ],
  "comment": "61 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the maximum $M_t$ of branching random walk in a space-inhomogeneous random environment on $\\mathbb{Z}$. In this model the branching rate while at some location $x\\in\\mathbb{Z}$ is randomized in an i.i.d.\\@ manner. We prove that there is a centering $\\widetilde{m}_t$ depending only on the environment such that $(M_t-\\widetilde{m}_t)_{t\\ge 0}$ is tight in an annealed sense.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-02T20:05:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80"
    ],
    "keywords": [
      "branching random walk",
      "space-inhomogeneous random environment",
      "branching rate",
      "annealed sense"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}