{
  "id": "1203.2368",
  "version": "v3",
  "published": "2012-03-11T19:38:08.000Z",
  "updated": "2013-01-31T07:48:19.000Z",
  "title": "Last passage percolation and traveling fronts",
  "authors": [
    "Francis Comets",
    "Jeremy Quastel",
    "Alejandro F. Ramirez"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a system of N particles with a stochastic dynamics introduced by Brunet and Derrida. The particles can be interpreted as last passage times in directed percolation on {1,...,N} of mean-field type. The particles remain grouped and move like a traveling wave, subject to discretization and driven by a random noise. As N increases, we obtain estimates for the speed of the front and its profile, for different laws of the driving noise. The Gumbel distribution plays a central role for the particle jumps, and we show that the scaling limit is a L\\'evy process in this case. The case of bounded jumps yields a completely different behavior.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-01-31T07:48:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "passage percolation",
      "traveling fronts",
      "gumbel distribution plays",
      "levy process",
      "passage times"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s10955-013-0779-8",
      "journal": "Journal of Statistical Physics",
      "year": 2013,
      "month": "Aug",
      "volume": 152,
      "number": 3,
      "pages": 419
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JSP...152..419C"
    }
  }
}