{
  "id": "math/0102206",
  "version": "v1",
  "published": "2001-02-27T04:14:01.000Z",
  "updated": "2001-02-27T04:14:01.000Z",
  "title": "Random walks with badly approximable numbers",
  "authors": [
    "Doug Hensley",
    "Francis Edward Su"
  ],
  "comment": "7 pages; to appear in DIMACS volume \"Unusual Applications of Number Theory\"; related work at http://www.math.hmc.edu/~su/papers.html",
  "journal": "DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 64 (2004), 95-101.",
  "categories": [
    "math.PR",
    "math.NT"
  ],
  "abstract": "Using the discrepancy metric, we analyze the rate of convergence of a random walk on the circle generated by d rotations, and establish sharp rates that show that badly approximable d-tuples in R^d give rise to walks with the fastest convergence. We use the discrepancy metric because the walk does not converge in total variation. For badly approximable d-tuples, the discrepancy is bounded above and below by (constant)k^(-d/2), where k is the number of steps in the random walk. We show how the constants depend on the d-tuple.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-02-27T04:14:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B15",
      "11J13",
      "11K38",
      "11K60"
    ],
    "keywords": [
      "random walk",
      "badly approximable numbers",
      "badly approximable d-tuples",
      "discrepancy metric",
      "fastest convergence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......2206H"
    }
  }
}