{
  "id": "2009.10810",
  "version": "v1",
  "published": "2020-09-22T20:55:47.000Z",
  "updated": "2020-09-22T20:55:47.000Z",
  "title": "On the number of contingency tables and the independence heuristic",
  "authors": [
    "Hanbaek Lyu",
    "Igor Pak"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.CO",
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We obtain sharp asymptotic estimates on the number of $n \\times n$ contingency tables with two linear margins $Cn$ and $BCn$. The results imply a second order phase transition on the number of such contingency tables, with a critical value at \\ts $B_{c}:=1 + \\sqrt{1+1/C}$. As a consequence, for \\ts $B>B_{c}$, we prove that the classical \\emph{independence heuristic} leads to a large undercounting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-22T20:55:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "contingency tables",
      "independence heuristic",
      "second order phase transition",
      "sharp asymptotic estimates",
      "linear margins"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}