{
  "id": "2006.03433",
  "version": "v1",
  "published": "2020-06-04T08:48:45.000Z",
  "updated": "2020-06-04T08:48:45.000Z",
  "title": "The speed of a biased random walk on a Galton-Watson tree is analytic",
  "authors": [
    "Adam Bowditch",
    "Yuki Tokushige"
  ],
  "comment": "11 pages, 1 figure. arXiv admin note: text overlap with arXiv:1906.07913",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that the speed of a biased random walk on a supercritical Galton-Watson tree conditioned to survive is analytic within the ballistic regime. This extends the previous work arXiv:1906.07913 in which it was shown that the speed is differentiable within the range of bias for which a central limit theorem holds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-04T08:48:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60K37",
      "60J10",
      "05C81"
    ],
    "keywords": [
      "biased random walk",
      "central limit theorem holds",
      "ballistic regime",
      "supercritical galton-watson tree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}