{
  "id": "math/0611607",
  "version": "v1",
  "published": "2006-11-20T14:04:59.000Z",
  "updated": "2006-11-20T14:04:59.000Z",
  "title": "On laws of large numbers for random walks",
  "authors": [
    "Anders Karlsson",
    "François Ledrappier"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117906000000296 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2006, Vol. 34, No. 5, 1693-1706",
  "doi": "10.1214/009117906000000296",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove a general noncommutative law of large numbers. This applies in particular to random walks on any locally finite homogeneous graph, as well as to Brownian motion on Riemannian manifolds which admit a compact quotient. It also generalizes Oseledec's multiplicative ergodic theorem. In addition, we show that $\\epsilon$-shadows of any ballistic random walk with finite moment on any group eventually intersect. Some related results concerning Coxeter groups and mapping class groups are recorded in the last section.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-20T14:04:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F99",
      "60B99",
      "37A30",
      "60J50",
      "60J65"
    ],
    "keywords": [
      "large numbers",
      "generalizes oseledecs multiplicative ergodic theorem",
      "related results concerning coxeter groups",
      "ballistic random walk",
      "finite moment"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11607K"
    }
  }
}