{
  "id": "1010.3092",
  "version": "v1",
  "published": "2010-10-15T08:21:12.000Z",
  "updated": "2010-10-15T08:21:12.000Z",
  "title": "A functional limit theorem for the profile of $b$-ary trees",
  "authors": [
    "Eva-Maria Schopp"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AAP640 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2010, Vol. 20, No. 3, 907-950",
  "doi": "10.1214/09-AAP640",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we prove a functional limit theorem for the weighted profile of a $b$-ary tree. For the proof we use classical martingales connected to branching Markov processes and a generalized version of the profile-polynomial martingale. By embedding, choosing weights and a branch factor in a right way, we finally rediscover the profiles of some well-known discrete time trees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-15T08:21:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional limit theorem",
      "ary tree",
      "well-known discrete time trees",
      "branching markov processes",
      "right way"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.3092S"
    }
  }
}