{
  "id": "math/0611911",
  "version": "v2",
  "published": "2006-11-29T11:38:02.000Z",
  "updated": "2008-04-13T15:56:54.000Z",
  "title": "Dimension and waiting time in rapidly mixing systems",
  "authors": [
    "S. Galatolo"
  ],
  "comment": "Revised version, very similar to the one is published",
  "journal": "Math. Res. Lett. (2007)",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that if a system has superpolynomial (faster than any power law) decay of correlations then the time $\\tau_{r}(x,x_{0})$ needed for a typical point $x$ to enter for the first time a ball $B(x_{0},r)$ centered in $x_{0},$ with small radius $r$ scales as the local dimension at $x_{0},$ i.e. $$\\underset{r\\to 0}{\\lim}\\frac{\\log \\tau_{r}(x,x_{0})}{-\\log r}=d_{\\mu }(x_{0}).$$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-13T15:56:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A25",
      "37C45"
    ],
    "keywords": [
      "rapidly mixing systems",
      "waiting time",
      "local dimension",
      "small radius",
      "first time"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11911G"
    }
  }
}