{
  "id": "1802.03428",
  "version": "v1",
  "published": "2018-02-07T23:12:49.000Z",
  "updated": "2018-02-07T23:12:49.000Z",
  "title": "Cover time for the frog model on trees",
  "authors": [
    "Christopher Hoffman",
    "Tobias Johnson",
    "Matthew Junge"
  ],
  "comment": "34 pages, 4 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "The frog model is a branching random walk on a graph in which particles branch only at unvisited sites. Consider an initial particle density of $\\mu$ on the full $d$-ary tree of height $n$. If $\\mu= \\Omega( d^2)$, all of the vertices are visited in time $\\Theta(n\\log n)$ with high probability. Conversely, if $\\mu = O(d)$ the cover time is $\\exp(\\Theta(\\sqrt n))$ with high probability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-07T23:12:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60J80",
      "60J10"
    ],
    "keywords": [
      "frog model",
      "cover time",
      "high probability",
      "initial particle density",
      "ary tree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}