{
  "id": "1906.07276",
  "version": "v1",
  "published": "2019-06-17T21:18:50.000Z",
  "updated": "2019-06-17T21:18:50.000Z",
  "title": "Limit law for the cover time of a random walk on a binary tree",
  "authors": [
    "Amir Dembo",
    "Jay Rosen",
    "Ofer Zeitouni"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $T_n$ denote the binary tree of depth $n$ augmented by an extra edge connected to its root. Let $C_n$ denote the cover time of $T_n$ by simple random walk. We prove that $\\sqrt{ \\mathcal{C}_{n} 2^{-(n+1) } } - m_n$ converges in distribution as $n\\to \\infty$, where $m_n$ is an explicit constant, and identify the limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-17T21:18:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cover time",
      "binary tree",
      "limit law",
      "simple random walk",
      "extra edge"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}