{
  "id": "1906.07913",
  "version": "v1",
  "published": "2019-06-19T04:46:08.000Z",
  "updated": "2019-06-19T04:46:08.000Z",
  "title": "Differentiability of the speed of biased random walks on Galton-Watson trees",
  "authors": [
    "Adam Bowditch",
    "Yuki Tokushige"
  ],
  "comment": "29 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that the speed of a $\\lambda$-biased random walk on a supercritical Galton-Watson tree is differentiable for $\\lambda$ such that the walk is ballistic and obeys a central limit theorem, and give an expression of the derivative using a certain $2$-dimensional Gaussian random variable. The proof heavily uses the renewal structure of Galton-Watson trees that was introduced by Lyons-Pemantle-Peres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-19T04:46:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "biased random walk",
      "differentiability",
      "central limit theorem",
      "renewal structure",
      "supercritical galton-watson tree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}