{
  "id": "math/0309011",
  "version": "v2",
  "published": "2003-08-31T20:35:05.000Z",
  "updated": "2004-04-27T00:29:03.000Z",
  "title": "Random walks on the torus with several generators",
  "authors": [
    "Timothy Prescott",
    "Francis Edward Su"
  ],
  "comment": "10 pages; related work at http://www.math.hmc.edu/~su/papers.html",
  "journal": "Random Structures and Algorithms 25 (2004), 336-345.",
  "doi": "10.1002/rsa.20029",
  "categories": [
    "math.PR"
  ],
  "abstract": "Our paper gives bounds for the rate of convergence for a class of random walks on the d-dimensional torus generated by a set of n vectors in R^d/Z^d. We give bounds on the discrepancy distance from Haar measure; our lower bound holds for all such walks, and if the generators arise from the rows of a \"badly approximable\" matrix, then there is a corresponding upper bound. The bounds are sharp for walks on the circle.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-04-27T00:29:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B15",
      "11J13",
      "11K38"
    ],
    "keywords": [
      "random walks",
      "lower bound holds",
      "generators arise",
      "haar measure",
      "corresponding upper bound"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9011P"
    }
  }
}