{
  "id": "1904.03667",
  "version": "v1",
  "published": "2019-04-07T15:09:57.000Z",
  "updated": "2019-04-07T15:09:57.000Z",
  "title": "Passage time of the frog model has a sublinear variance",
  "authors": [
    "Van Hao Can",
    "Shuta Nakajima"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we show that the passage time in the frog model on $\\mathbb{Z}^d$ with $d\\geq 2$ has a sublinear variance. The proof is based on the method introduced in \\cite{DHS} combining with tessellation arguments to estimate the martingale difference. We also apply this method to get the linearity of the lengths of optimal paths.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-07T15:09:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sublinear variance",
      "frog model",
      "passage time",
      "tessellation arguments",
      "martingale difference"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}