{
  "id": "1905.00624",
  "version": "v1",
  "published": "2019-05-02T08:59:05.000Z",
  "updated": "2019-05-02T08:59:05.000Z",
  "title": "The critical window in random digraphs",
  "authors": [
    "Matthew Coulson"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We consider the component structure of the random digraph $D(n,p)$ inside the critical window $p = n^{-1} + \\lambda n^{-4/3}$.We show that the largest component $\\mathcal{C}_1$ has size of order $n^{1/3}$ in this range. In particular we give explicit bounds on the tail probabilities of $|\\mathcal{C}_1|n^{-1/3}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-02T08:59:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random digraph",
      "critical window",
      "component structure",
      "largest component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}