{
  "id": "0905.3545",
  "version": "v1",
  "published": "2009-05-21T18:54:17.000Z",
  "updated": "2009-05-21T18:54:17.000Z",
  "title": "A phase transition for the heights of a fragmentation tree",
  "authors": [
    "Adrien Joseph"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We provide information about the asymptotic regimes for a homogeneous fragmentation of a finite set. We establish a phase transition for the asymptotic behaviours of the shattering times, defined as the first instants when all the blocks of the partition process have cardinality less than a fixed integer. Our results may be applied to the study of certain random split trees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-21T18:54:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15"
    ],
    "keywords": [
      "phase transition",
      "fragmentation tree",
      "random split trees",
      "asymptotic regimes",
      "partition process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}