{
  "id": "math/0406078",
  "version": "v3",
  "published": "2004-06-04T15:05:53.000Z",
  "updated": "2005-02-23T15:12:26.000Z",
  "title": "Self-Similar Corrections to the Ergodic Theorem for the Pascal-Adic Transformation",
  "authors": [
    "Elise Janvresse",
    "Thierry de la Rue",
    "Yvan Velenik"
  ],
  "comment": "version to appear in Stochastics and Dynamics. We added a discussion on the links with Conway 10,000$ recursive sequence",
  "journal": "Stochastics and dynamics 5, no.1, pp 1-25 (2005)",
  "doi": "10.1142/S0219493705001250",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Let T be the Pascal-adic transformation. For any measurable function g, we consider the corrections to the ergodic theorem sum_{k=0}^{j-1} g(T^k x) - j/l sum_{k=0}^{l-1} g(T^k x). When seen as graphs of functions defined on {0,...,l-1}, we show for a suitable class of functions g that these quantities, once properly renormalized, converge to (part of) the graph of a self-affine function. The latter only depends on the ergodic component of x, and is a deformation of the so-called Blancmange function. We also briefly describe the links with a series of works on Conway recursive $10,000 sequence.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-02-23T15:12:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30",
      "28A80"
    ],
    "keywords": [
      "ergodic theorem",
      "pascal-adic transformation",
      "self-similar corrections",
      "self-affine function",
      "ergodic component"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6078J"
    }
  }
}