{
  "id": "1202.2665",
  "version": "v2",
  "published": "2012-02-13T09:09:35.000Z",
  "updated": "2012-10-04T06:20:50.000Z",
  "title": "Monotonicity in first-passage percolation",
  "authors": [
    "Jean-Baptiste Gouéré"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider standard first-passage percolation on $\\Z^d$. Let $e_1$ be the first coordinate vector. Let $a(n)$ be the expected passage time from the origin to $ne_1$. In this short paper, we note that $a(n)$ is increasing under some strong condition on the support of the law of the passage times on the edges.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-04T06:20:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monotonicity",
      "standard first-passage percolation",
      "first coordinate vector",
      "short paper",
      "strong condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.2665G"
    }
  }
}