{
  "id": "math/0203262",
  "version": "v5",
  "published": "2002-03-25T19:39:29.000Z",
  "updated": "2007-05-25T18:44:26.000Z",
  "title": "First Passage Percolation Has Sublinear Distance Variance",
  "authors": [
    "Itai Benjamini",
    "Gil Kalai",
    "Oded Schramm"
  ],
  "comment": "Replaced theorem 2 (which was incorrect) by a new theorem",
  "journal": "AnnalsProbab.31:197-1978,2003",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let $0<a<b<\\infty$, and for each edge $e$ of $Z^d$ let $\\omega_e=a$ or $\\omega_e=b$, each with probability 1/2, independently. This induces a random metric $\\dist_\\omega$ on the vertices of $Z^d$, called first passage percolation. We prove that for $d>1$ the distance $dist_\\omega(0,v)$ from the origin to a vertex $v$, $|v|>2$, has variance bounded by $C |v|/\\log|v|$, where $C=C(a,b,d)$ is a constant which may only depend on $a$, $b$ and $d$. Some related variants are also discussed",
  "revisions": [
    {
      "version": "v5",
      "updated": "2007-05-25T18:44:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60B15"
    ],
    "keywords": [
      "first passage percolation",
      "sublinear distance variance",
      "random metric",
      "probability",
      "related variants"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 610525,
      "adsabs": "2002math......3262B"
    }
  }
}