{
  "id": "math/0701259",
  "version": "v1",
  "published": "2007-01-09T17:37:56.000Z",
  "updated": "2007-01-09T17:37:56.000Z",
  "title": "Precise logarithmic asymptotics for the right tails of some limit random variables for random trees",
  "authors": [
    "James Allen Fill",
    "Svante Janson"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "For certain random variables that arise as limits of functionals of random finite trees, we obtain precise asymptotics for the logarithm of the right-hand tail. Our results are based on the facts (i) that the random variables we study can be represented as functionals of a Brownian excursion and (ii) that a large deviation principle with good rate function is known explicitly for Brownian excursion. Examples include limit distributions of the total path length and of the Wiener index in conditioned Galton-Watson trees (also known as simply generated trees). In the case of Wiener index (where we recover results proved by Svante Janson and Philippe Chassaing by a different method) and for some other examples, a key constant is expressed as the solution to a certain optimization problem, but the constant's precise value remains unknown.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-09T17:37:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60C05",
      "60J65"
    ],
    "keywords": [
      "limit random variables",
      "precise logarithmic asymptotics",
      "right tails",
      "random trees",
      "constants precise value remains unknown"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1259F"
    }
  }
}