{
  "id": "0706.0496",
  "version": "v1",
  "published": "2007-06-04T18:40:46.000Z",
  "updated": "2007-06-04T18:40:46.000Z",
  "title": "The Order of the Giant Component of Random Hypergraphs",
  "authors": [
    "Michael Behrisch",
    "Amin Coja-Oghlan",
    "Mihyun Kang"
  ],
  "comment": "28 pages, 1 figure",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We establish central and local limit theorems for the number of vertices in the largest component of a random $d$-uniform hypergraph $\\hnp$ with edge probability $p=c/\\binnd$, where $(d-1)^{-1}+\\eps<c<\\infty$. The proof relies on a new, purely probabilistic approach, and is based on Stein's method as well as exposing the edges of $H_d(n,p)$ in several rounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-04T18:40:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80"
    ],
    "keywords": [
      "random hypergraphs",
      "giant component",
      "local limit theorems",
      "uniform hypergraph",
      "largest component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.0496B"
    }
  }
}