{
  "id": "0808.3021",
  "version": "v1",
  "published": "2008-08-22T01:26:53.000Z",
  "updated": "2008-08-22T01:26:53.000Z",
  "title": "On the concentration and the convergence rate with a moment condition in first passage percolation",
  "authors": [
    "Yu Zhang"
  ],
  "comment": "27 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the first passage percolation model on the ${\\bf Z}^d$ lattice. In this model, we assign independently to each edge $e$ a non-negative passage time $t(e)$ with a common distribution $F$. Let $a_{0,n}$ be the passage time from the origin to $(n,0,..., 0)$. Under the exponential tail assumption, Kesten (1993) and Talagrand (1995) investigated the concentration of $a_{0,n}$ from its mean using different methods. With this concentration and the exponential tail assumption, Alexander gave an estimate for the convergence rate for ${\\bf E} a_{0,n}$. In this paper, focusing on a moment condition, we reinvestigate the concentration and the convergence rate for $a_{0,n}$ using a special martingale structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-22T01:26:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "convergence rate",
      "moment condition",
      "concentration",
      "exponential tail assumption",
      "first passage percolation model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.3021Z"
    }
  }
}