{
  "id": "math/0703670",
  "version": "v1",
  "published": "2007-03-22T16:53:24.000Z",
  "updated": "2007-03-22T16:53:24.000Z",
  "title": "Local limit theorem for nonuniformly partially hyperbolic skew-products, and Farey sequences",
  "authors": [
    "Sebastien Gouezel"
  ],
  "comment": "55 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study skew-products of the form (x,\\omega)\\mapsto (Tx, \\omega+\\phi(x)) where T is a nonuniformly expanding map on a space X, preserving a (possibly singular) probability measure \\tilde\\mu, and \\phi:X\\to S^1 is a C^1 function. Under mild assumptions on \\tilde\\mu and \\phi, we prove that such a map is exponentially mixing, and satisfies the central and local limit theorems. These results apply to a random walk related to the Farey sequence, thereby answering a question of Guivarc'h and Raugi.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-22T16:53:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A25",
      "37A30",
      "37A50",
      "37D25",
      "37D30"
    ],
    "keywords": [
      "local limit theorem",
      "nonuniformly partially hyperbolic skew-products",
      "farey sequence",
      "study skew-products",
      "random walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3670G"
    }
  }
}