{
  "id": "1905.05613",
  "version": "v1",
  "published": "2019-05-14T13:55:18.000Z",
  "updated": "2019-05-14T13:55:18.000Z",
  "title": "On the Cover time of $λ$-biased walk on supercritical Galton-Watson trees",
  "authors": [
    "Tianyi Bai"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we study the time required for a $\\lambda$-biased ($\\lambda>1$) walk to visit all nodes of a supercritical Galton-Watson tree up to generation $n$. Inspired by the extremal landscape approach in [Cortines et al. 2018] for simple random walk on binary trees, we establish the near-independent nature of extremal points for the $\\lambda$-biased walk, and deduce the scaling limit of the cover time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-14T13:55:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supercritical galton-watson tree",
      "cover time",
      "biased walk",
      "extremal landscape approach",
      "simple random walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}