{
  "id": "1112.1250",
  "version": "v1",
  "published": "2011-12-06T12:24:48.000Z",
  "updated": "2011-12-06T12:24:48.000Z",
  "title": "Degree distribution in the lower levels of the uniform recursive tree",
  "authors": [
    "Ágnes Backhausz",
    "Tamás F. Móri"
  ],
  "comment": "8 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this note we consider the $k$th level of the uniform random recursive tree after $n$ steps, and prove that the proportion of nodes with degree greater than $t\\log n$ converges to $(1-t)^k$ almost surely, as $n\\to\\infty$, for every $t\\in(0,1)$. In addition, we show that the number of degree $d$ nodes in the first level is asymptotically Poisson distributed with mean 1; moreover, they are asymptotically independent for $d=1,2,...$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-06T12:24:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60C05",
      "60F15"
    ],
    "keywords": [
      "uniform recursive tree",
      "degree distribution",
      "lower levels",
      "uniform random recursive tree",
      "th level"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1250B"
    }
  }
}