{
  "id": "1808.00735",
  "version": "v1",
  "published": "2018-08-02T09:48:53.000Z",
  "updated": "2018-08-02T09:48:53.000Z",
  "title": "Limit theorems for some skew products with mixing base maps",
  "authors": [
    "Yeor Hafouta"
  ],
  "categories": [
    "math.PR",
    "math.DS"
  ],
  "abstract": "We obtain central limit theorem, local limit theorems and renewal theorems for stationary processes generated by skew product maps $T(\\om,x)=(\\te\\om,T_\\om x)$ together with a $T$-invariant measure, whose base map $\\te$ satisfies certain topological and mixing conditions and the maps $T_\\om$ on the fibers are certain non-singular distance expanding maps. Our results hold true when $\\te$ is either a sufficiently fast mixing Markov shift or a (non-uniform) Young tower with at least one periodic point and polynomial tails. %In fact, our conditions will be satisfied %when $\\om$ is the whole orbit the towers. The proofs are based on the random complex Ruelle-Perron-Frobenius theorem from \\cite{book} applied with appropriate random transfer operators generated by $T_\\om$, together with certain regularity assumptions (as functions of $\\om$) of these operators. Limit theorems for deterministic processes whose distributions on the fibers are generated by Markov chains with transition operators satisfying a random version of the Doeblin condition will also be obtained. The main innovation in this paper is that the results hold true even though the spectral theory used in \\cite{Aimino} does not seem to be applicable, and the dual of the Koopman operator of $T$ (with respect to the invariant measure) does not seem to have a spectral gap.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-02T09:48:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "limit theorem",
      "mixing base maps",
      "skew product",
      "fast mixing markov shift",
      "results hold true"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}