{
  "id": "1706.09167",
  "version": "v1",
  "published": "2017-06-28T08:29:57.000Z",
  "updated": "2017-06-28T08:29:57.000Z",
  "title": "Central Limit Theorems for group actions which are exponentially mixing of all orders",
  "authors": [
    "Michael Björklund",
    "Alexander Gorodnik"
  ],
  "comment": "20 pages, no figures. Comments are welcome!",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "In this paper we establish a general dynamical Central Limit Theorem (CLT) for group actions which are exponentially mixing of all orders. In particular, the main result applies to Cartan flows on finite-volume quotients of simple Lie groups. Our proof uses a novel relativization of the classical method of cumulants, which should be of independent interest. As a sample application of our techniques, we show that the CLT holds along lacunary samples of the horocycle flow on finite-area hyperbolic surfaces applied to any smooth compactly supported function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-28T08:29:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "group actions",
      "exponentially mixing",
      "general dynamical central limit theorem",
      "finite-area hyperbolic surfaces",
      "main result applies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}