{
  "id": "1902.08958",
  "version": "v1",
  "published": "2019-02-24T14:49:00.000Z",
  "updated": "2019-02-24T14:49:00.000Z",
  "title": "Necessary and sufficient condition for $\\cM_2$-convergence to a Lévy process for billiards with cusps at flat points",
  "authors": [
    "Paul Jung",
    "Ian Melbourne",
    "Françoise Pène",
    "Paulo Varandas",
    "Hong-Kun Zhang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider a class of planar dispersing billiards with a cusp at a point of vanishing curvature. Convergence to a stable law and to the corresponding L\\'evy process in the $\\cM_1$ and $\\cM_2$ Skorohod topologies has been studied in recent work. Here we show that certain sufficient conditions for $\\cM_2$-convergence are also necessary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-24T14:49:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sufficient condition",
      "lévy process",
      "flat points",
      "convergence",
      "planar dispersing billiards"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}