{
  "id": "1606.06536",
  "version": "v1",
  "published": "2016-06-21T12:30:18.000Z",
  "updated": "2016-06-21T12:30:18.000Z",
  "title": "Asymptotics of heights in random trees constructed by aggregation",
  "authors": [
    "Bénédicte Haas"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "To each sequence $(a_n)$ of positive real numbers we associate a growing sequence $(T_n)$ of continuous trees built recursively by gluing at step $n$ a segment of length $a_n$ on a uniform point of the pre-existing tree, starting from a segment $T_1$ of length $a_1$. Previous works on that model focus on the influence of $(a_n)$ on the compactness and Hausdorff dimension of the limiting tree. Here we consider the cases where the sequence $(a_n)$ is regularly varying with a non-negative index, so that the sequence $(T_n)$ exploses. We determine the asymptotics of the height of $T_n$ and of the subtrees of $T_n$ spanned by the root and $\\ell$ points picked uniformly at random and independently in $T_n$, for all $\\ell \\in \\mathbb N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-21T12:30:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random trees",
      "asymptotics",
      "aggregation",
      "hausdorff dimension",
      "model focus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}