{
  "id": "2008.09226",
  "version": "v1",
  "published": "2020-08-20T23:22:17.000Z",
  "updated": "2020-08-20T23:22:17.000Z",
  "title": "On the minimal drift for recurrence in the frog model on $d$-ary trees",
  "authors": [
    "Chengkun Guo",
    "Si Tang",
    "Ningxi Wei"
  ],
  "comment": "21 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the recurrence of one-per-site frog model $\\text{FM}(d, p)$ on a $d$-ary tree with drift parameter $p\\in [0,1]$, which determines the bias of frogs' random walks. We are interested in the minimal drift $p_{d}$ so that the frog model is recurrent. Using a coupling argument together with a generating function technique, we prove that for all $d \\ge 2$, $p_{d}\\le 1/3$, which is the optimal universal upper bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-20T23:22:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60J80",
      "60J10",
      "82B26"
    ],
    "keywords": [
      "minimal drift",
      "ary tree",
      "recurrence",
      "optimal universal upper bound",
      "one-per-site frog model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}