{
  "id": "1811.04849",
  "version": "v1",
  "published": "2018-11-12T16:46:02.000Z",
  "updated": "2018-11-12T16:46:02.000Z",
  "title": "Regularity results of the speed of biased random walks on Galton-Watson trees",
  "authors": [
    "Yuki Tokushige"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that the speed of $\\lambda$-biased random walks on a supercritical Galton-Watson tree without leaves is differentiable when $\\lambda\\in(0,1)$, 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": "2018-11-12T16:46:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "biased random walks",
      "regularity results",
      "supercritical galton-watson tree",
      "renewal structure",
      "expression"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}