{
  "id": "0807.0839",
  "version": "v2",
  "published": "2008-07-05T02:47:39.000Z",
  "updated": "2008-07-13T08:16:59.000Z",
  "title": "On a Lower Bound for the Time Constant of First-Passage Percolation",
  "authors": [
    "Xian-Yuan Wu",
    "Ping Feng"
  ],
  "comment": "7 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the Bernoulli first-passage percolation on $\\mathbb Z^d (d\\ge 2)$. That is, the edge passage time is taken independently to be 1 with probability $1-p$ and 0 otherwise. Let ${\\mu(p)}$ be the time constant. We prove in this paper that \\[ \\mu(p_1)-\\mu({p_2})\\ge \\frac{\\mu(p_2)}{1-p_2}(p_2-p_1)\\] for all $ 0\\leq p_1<p_2< 1$ by using Russo's formula.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-07-13T08:16:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "time constant",
      "lower bound",
      "edge passage time",
      "bernoulli first-passage percolation",
      "russos formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.0839W"
    }
  }
}