{
  "id": "math/0409225",
  "version": "v1",
  "published": "2004-09-14T13:17:21.000Z",
  "updated": "2004-09-14T13:17:21.000Z",
  "title": "On Long Range Percolation with Heavy Tails",
  "authors": [
    "S. Friedli",
    "N. B. N. de Lima",
    "V. Sidoravicius"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Consider independent long range percolation on $\\mathbf{Z}^2$, where horizontal and vertical edges of length $n$ are open with probability $p_n$. We show that if $\\limsup_{n\\to\\infty}p_n>0,$ then there exists an integer $N$ such that $P_N(0\\leftrightarrow \\infty)>0$, where $P_N$ is the truncated measure obtained by taking $p_{N,n}=p_n$ for $n \\leq N$ and $p_{N,n}=0$ for all $n> N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-14T13:17:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B44"
    ],
    "keywords": [
      "heavy tails",
      "independent long range percolation",
      "horizontal",
      "vertical edges",
      "probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9225F"
    }
  }
}