{
  "id": "1612.08581",
  "version": "v1",
  "published": "2016-12-27T11:34:46.000Z",
  "updated": "2016-12-27T11:34:46.000Z",
  "title": "Upper tail estimates for the first passage time in the frog model",
  "authors": [
    "Naoki Kubota"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the so-called frog model with random initial configurations. The dynamics of this model are described as follows: Some particles are randomly assigned on any site of the multidimensional cubic lattice $\\mathbb{Z}^d$ ($d \\geq 2$). Initially, only particles at the origin are active, and these independently perform simple random walks on $\\mathbb{Z}^d$. Other particles are sleeping and do not move. When sleeping particles are attacked by an active particle, they become active and start moving in a similar fashion. In this context, the aim of this paper is to obtain some tail estimates for the first passage time at which an active particle reaches a target site. As a consequence, we derive order of intervals of initial positions of particles attaining the first passage time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-27T11:34:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60F99"
    ],
    "keywords": [
      "first passage time",
      "upper tail estimates",
      "frog model",
      "independently perform simple random walks",
      "active particle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}