{
  "id": "1705.10550",
  "version": "v1",
  "published": "2017-05-30T11:26:28.000Z",
  "updated": "2017-05-30T11:26:28.000Z",
  "title": "Diffuse Behaviour of Ergodic Sums Over Rotations",
  "authors": [
    "Jean-Pierre Conze",
    "Stefano Isola",
    "Stéphane Le Borgne"
  ],
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "For a rotation by an irrational $\\alpha$ on the circle and a BV function $\\varphi$, we study the variance of the ergodic sums $S_L \\varphi(x) := \\sum_{j=0}^{L -1} \\, \\varphi(x + j\\alpha)$. When $\\alpha$ is not of constant type, we construct sequences $(L_N)$ such that, at some scale, the ergodic sums $S_{L_N} \\varphi$ satisfy an ASIP. Explicit non-degenerate examples are given, with an application to the rectangular periodic billiard in the plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-30T11:26:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ergodic sums",
      "diffuse behaviour",
      "rectangular periodic billiard",
      "explicit non-degenerate examples",
      "bv function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}