{
  "id": "2102.04083",
  "version": "v1",
  "published": "2021-02-08T09:44:56.000Z",
  "updated": "2021-02-08T09:44:56.000Z",
  "title": "On Convergence of Random Walks on Moduli Space",
  "authors": [
    "Roland Prohaska"
  ],
  "comment": "7 pages",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "The purpose of this note is to establish convergence of random walks on the moduli space of Abelian differentials on compact Riemann surfaces in two different modes: convergence of the $n$-step distributions towards the normalized Masur-Veech measure from almost every starting point, and almost sure pathwise equidistribution towards the affine invariant measure on the $SL_2(\\mathbb{R})$-orbit closure of an arbitrary starting point. These are analogues to previous results for random walks on homogeneous spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-08T09:44:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B15",
      "32G15",
      "60G50",
      "22F10"
    ],
    "keywords": [
      "random walks",
      "moduli space",
      "convergence",
      "compact riemann surfaces",
      "affine invariant measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}