{
  "id": "math/0110280",
  "version": "v1",
  "published": "2001-10-25T15:37:12.000Z",
  "updated": "2001-10-25T15:37:12.000Z",
  "title": "The shape theorem for the frog model with random initial configuration",
  "authors": [
    "O. S. M. Alves",
    "F. P. Machado",
    "S. Yu. Popov",
    "K. Ravishankar"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove a shape theorem for a growing set of simple random walks on Z^d, known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent discrete time SRWs, and sleeping particles, which do not move. When a sleeping particle is hit by an active particle, the former becomes active as well. Initially, a random number of particles is placed into each site. At time 0 all particles are sleeping, except for those placed at the origin. We prove that the set of all sites visited by active particles, rescaled by the elapsed time, converges to a compact convex set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-10-25T15:37:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60J10"
    ],
    "keywords": [
      "random initial configuration",
      "frog model",
      "shape theorem",
      "active particle",
      "perform independent discrete time srws"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10280A"
    }
  }
}