{
  "id": "1306.1197",
  "version": "v2",
  "published": "2013-06-05T18:04:28.000Z",
  "updated": "2014-10-23T02:17:52.000Z",
  "title": "Sublinear variance in first-passage percolation for general distributions",
  "authors": [
    "Michael Damron",
    "Jack Hanson",
    "Philippe Sosoe"
  ],
  "comment": "32 pages. We added a proof sketch and fixed the proof of Theorem 2.3 and the bound on term (6.18)",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that the variance of the passage time from the origin to a point x in first-passage percolation on Z^d is sublinear in the distance to x when d \\geq 2, obeying the bound Cx/(log x), under minimal assumptions on the edge-weight distribution. The proof applies equally to absolutely continuous, discrete and singular continuous distributions and mixtures thereof, and requires only 2+log moments. The main result extends work of Benjamini-Kalai-Schramm and Benaim-Rossignol.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-05T18:04:28.000Z",
      "comment": "29 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-23T02:17:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first-passage percolation",
      "sublinear variance",
      "general distributions",
      "main result extends work",
      "passage time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.1197D"
    }
  }
}