{
  "id": "1002.3896",
  "version": "v1",
  "published": "2010-02-22T15:52:11.000Z",
  "updated": "2010-02-22T15:52:11.000Z",
  "title": "Almost sure asymptotics for the random binary search tree",
  "authors": [
    "Matthew I. Roberts"
  ],
  "comment": "12 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a (random permutation model) binary search tree with n nodes and give asymptotics on the loglog scale for the height H_n and saturation level h_n of the tree as n\\to\\infty, both almost surely and in probability. We then consider the number F_n of particles at level H_n at time n, and show that F_n is unbounded almost surely.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-22T15:52:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "68W40",
      "60C05"
    ],
    "keywords": [
      "random binary search tree",
      "sure asymptotics",
      "random permutation model",
      "loglog scale",
      "saturation level"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.3896R"
    }
  }
}