{
  "id": "1709.00038",
  "version": "v1",
  "published": "2017-08-31T18:46:13.000Z",
  "updated": "2017-08-31T18:46:13.000Z",
  "title": "Recurrence and Transience of Frogs with Drift on $\\mathbb{Z}^d$",
  "authors": [
    "Christian Döbler",
    "Nina Gantert",
    "Thomas Höfelsauer",
    "Serguei Popov",
    "Felizitas Weidner"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the frog model on $\\mathbb{Z}^d$ with drift in dimension $d \\geq 2$ and establish the existence of transient and recurrent regimes depending on the transition probabilities. We focus on a model in which the particles perform nearest neighbour random walks which are balanced in all but one direction. This gives a model with two parameters. We present conditions on the parameters for recurrence and transience, revealing interesting differences between dimension $d=2$ and dimension $d \\geq 3$. Our proofs make use of (refined) couplings with branching random walks for the transience, and with percolation for the recurrence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-31T18:46:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "recurrence",
      "transience",
      "particles perform nearest neighbour random",
      "perform nearest neighbour random walks",
      "frog model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}