{
  "id": "1910.05133",
  "version": "v1",
  "published": "2019-10-11T12:39:47.000Z",
  "updated": "2019-10-11T12:39:47.000Z",
  "title": "The frog model on non-amenable trees",
  "authors": [
    "Marcus Michelen",
    "Josh Rosenberg"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We examine an interacting particle system on trees commonly referred to as the frog model. For its initial state, it begins with a single active particle at the root and i.i.d. $\\mathrm{Poiss}(\\lambda)$ many inactive particles at each non-root vertex. Active particles perform discrete time simple random walk and in the process activate any inactive particles they encounter. We show that for $\\textit{every}$ non-amenable tree with bounded degree there exists a phase transition from transience to recurrence (with a non-trivial intermediate phase sometimes sandwiched in between) as $\\lambda$ varies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-11T12:39:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "frog model",
      "non-amenable tree",
      "particles perform discrete time simple",
      "discrete time simple random walk",
      "perform discrete time simple random"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}