{
  "id": "2003.12018",
  "version": "v1",
  "published": "2020-03-26T16:33:46.000Z",
  "updated": "2020-03-26T16:33:46.000Z",
  "title": "The asymptotic distribution of cluster sizes for supercritical percolation on random split trees",
  "authors": [
    "Gabriel Berzunza",
    "Cecilia Holmgren"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the model of random trees introduced by Devroye (1999), the so-called random split trees. The model encompasses many important randomized algorithms and data structures. We then perform supercritical Bernoulli bond-percolation on those trees and obtain a precise weak limit theorem for the sizes of the largest clusters. We also show that the approach developed in this work may be useful for studying percolation on other classes of trees with logarithmic height, for instance, we study also the case of $d$-regular trees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-26T16:33:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "60F05",
      "60K35",
      "68P05",
      "05C05",
      "05C80"
    ],
    "keywords": [
      "random split trees",
      "asymptotic distribution",
      "cluster sizes",
      "supercritical percolation",
      "precise weak limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}