{
  "id": "0904.1005",
  "version": "v2",
  "published": "2009-04-06T20:20:22.000Z",
  "updated": "2010-06-29T22:31:22.000Z",
  "title": "Strong law of large numbers on graphs and groups",
  "authors": [
    "Natalia Mosina",
    "Alexander Ushakov"
  ],
  "comment": "29 pages, 2 figures, new references added, Introduction revised, Chernoff-like bound added",
  "categories": [
    "math.PR",
    "math.GR"
  ],
  "abstract": "We consider (graph-)group-valued random element $\\xi$, discuss the properties of a mean-set $\\ME(\\xi)$, and prove the generalization of the strong law of large numbers for graphs and groups. Furthermore, we prove an analogue of the classical Chebyshev's inequality for $\\xi$ and Chernoff-like asymptotic bounds. In addition, we prove several results about configurations of mean-sets in graphs and discuss computational problems together with methods of computing mean-sets in practice and propose an algorithm for such computation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-29T22:31:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B99",
      "20P05"
    ],
    "keywords": [
      "large numbers",
      "strong law",
      "group-valued random element",
      "classical chebyshevs inequality",
      "computational problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1005M"
    }
  }
}