{
  "id": "1703.10652",
  "version": "v1",
  "published": "2017-03-30T19:51:08.000Z",
  "updated": "2017-03-30T19:51:08.000Z",
  "title": "Most trees are short and fat",
  "authors": [
    "Louigi Addario-Berry"
  ],
  "comment": "19 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This work proves new probability bounds relating to the height, width, and size of Galton-Watson trees. For example, if $T$ is any Galton-Watson tree, and $H$, $W$, and $|T|$ are the height, width, and size of $T$, respectively, then $H/W$ has sub-exponential tails and $H/|T|^{1/2}$ has sub-Gaussian tails. Although our methods apply without any assumptions on the offspring distribution, when information is provided about the distribution the method can be adapted accordingly, and always seems to yield tight bounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-30T19:51:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60G50",
      "60E15",
      "05C05"
    ],
    "keywords": [
      "galton-watson tree",
      "yield tight bounds",
      "sub-gaussian tails",
      "probability bounds",
      "sub-exponential tails"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}