{
  "id": "math/0211117",
  "version": "v2",
  "published": "2002-11-06T17:52:17.000Z",
  "updated": "2002-12-06T16:23:56.000Z",
  "title": "Central limit theorem and stable laws for intermittent maps",
  "authors": [
    "Sebastien Gouezel"
  ],
  "comment": "42 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In the setting of abstract Markov maps, we prove results concerning the convergence of renormalized Birkhoff sums to normal laws or stable laws. They apply to one-dimensional maps with a neutral fixed point at 0 of the form $x+x^{1+\\alpha}$, for $\\alpha\\in (0,1)$. In particular, for $\\alpha>1/2$, we show that the Birkhoff sums of a H\\\"older observable $f$ converge to a normal law or a stable law, depending on whether $f(0)=0$ or $f(0)\\not=0$. The proof uses spectral techniques introduced by Sarig, and Wiener's Lemma in noncommutative Banach algebras.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-12-06T16:23:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30",
      "37A50",
      "37C30",
      "37E05",
      "47A56",
      "60F05"
    ],
    "keywords": [
      "central limit theorem",
      "stable law",
      "intermittent maps",
      "normal law",
      "abstract markov maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11117G"
    }
  }
}