{
  "id": "1112.0510",
  "version": "v1",
  "published": "2011-12-02T17:14:52.000Z",
  "updated": "2011-12-02T17:14:52.000Z",
  "title": "Simply generated trees, conditioned Galton--Watson trees, random allocations and condensation",
  "authors": [
    "Svante Janson"
  ],
  "comment": "146 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give a unified treatment of the limit, as the size tends to infinity, of simply generated random trees, including both the well-known result in the standard case of critical Galton--Watson trees and similar but less well-known results in the other cases (i.e., when no equivalent critical Galton--Watson tree exists). There is a well-defined limit in the form of an infinite random tree in all cases; for critical Galton--Watson trees this tree is locally finite but for the other cases the random limit has exactly one node of infinite degree. The proofs use a well-known connection to a random allocation model that we call balls-in-boxes, and we prove corresponding theorems for this model. This survey paper contains many known results from many different sources, together with some new results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-02T17:14:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C50",
      "05C05",
      "60F05",
      "60J80"
    ],
    "keywords": [
      "conditioned galton-watson trees",
      "simply generated trees",
      "condensation",
      "well-known result",
      "random allocation model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 146,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.0510J"
    }
  }
}