{
  "id": "2006.08567",
  "version": "v1",
  "published": "2020-06-15T17:31:54.000Z",
  "updated": "2020-06-15T17:31:54.000Z",
  "title": "Ergodic cocycles of IDPFT systems and nonsingular Gaussian actions",
  "authors": [
    "Alexandre I. Danilenko",
    "Mariusz Lemańczyk"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "It is proved that each Gaussian cocycle over a mildly mixing Gaussian transformation is either a Gaussian coboundary or sharply weak mixing. The class of nonsingular infinite direct products $T$ of transformations $T_n$, $n\\in\\Bbb N$, of finite type (IDPFT) is studied. It is shown that if $T_n$ is mildly mixing, $n\\in\\Bbb N$, the sequence of the Radon-Nikodym derivatives of $T_n$ is asymptotically translation quasi-invariant and $T$ is conservative then the Maharam extension of $T$ is sharply weak mixing. This techniques provides a new approach to the nonsingular Gaussian transformations studied recently by Arano, Isono and Marrakchi.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-15T17:31:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A40"
    ],
    "keywords": [
      "nonsingular gaussian actions",
      "idpft systems",
      "ergodic cocycles",
      "nonsingular infinite direct products",
      "nonsingular gaussian transformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}