{
  "id": "math/0401073",
  "version": "v1",
  "published": "2004-01-08T11:02:18.000Z",
  "updated": "2004-01-08T11:02:18.000Z",
  "title": "Asymptotic expansions in $n^{-1}$ for percolation critical values on the $n$-cube and $\\mathbb{Z}^n$",
  "authors": [
    "Remco van der Hofstad",
    "Gordon Slade"
  ],
  "comment": "26 pages, 2 figures",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We use the lace expansion to prove that the critical values for nearest-neighbour bond percolation on the $n$-cube $\\{0,1\\}^n$ and on $\\mathbb{Z}^n$ have asymptotic expansions, with rational coefficients, to all orders in powers of $n^{-1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-01-08T11:02:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60K35",
      "82B43"
    ],
    "keywords": [
      "percolation critical values",
      "asymptotic expansions",
      "nearest-neighbour bond percolation",
      "lace expansion",
      "rational coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1073V"
    }
  }
}