{
  "id": "2009.08185",
  "version": "v1",
  "published": "2020-09-17T09:55:07.000Z",
  "updated": "2020-09-17T09:55:07.000Z",
  "title": "Global Regime for General Additive Functionals of Conditioned Bienaym{é}-Galton-Watson Trees",
  "authors": [
    "Romain Abraham",
    "Jean-François Delmas",
    "Michel Nassif"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We give an invariance principle for very general additive functionals of conditioned Bienaym{\\'e}-Galton-Watson trees in the global regime when the offspring distribution lies in the domain of attraction of a stable distribution, the limit being an additive functional of a stable L{\\'e}vy tree. This includes the case when the offspring distribution has finite variance (the L{\\'e}vy tree being then the Brownian tree). We also describe, using an integral test, a phase transition for toll functions depending on the size and height.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-17T09:55:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general additive functionals",
      "global regime",
      "conditioned bienaym",
      "vy tree",
      "invariance principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}