{
  "id": "1606.07664",
  "version": "v1",
  "published": "2016-06-24T12:46:54.000Z",
  "updated": "2016-06-24T12:46:54.000Z",
  "title": "A Glivenko-Cantelli Theorem for almost additive functions",
  "authors": [
    "Christoph Schumacher",
    "Fabian Schwarzenberger",
    "Ivan Veselic"
  ],
  "comment": "31 pages, to appear in Stochastic Processes and Applications",
  "doi": "10.1016/j.spa.2016.06.005",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We develop a Glivenko--Cantelli theory for monotone, almost additive functions of i.\\,i.\\,d.\\ sequences of random variables indexed by~$\\Z^d$. Under certain conditions on the random sequence, short range correlations are allowed as well. We have an explicit error estimate, consisting of a probabilistic and a geometric part. We apply the results to yield uniform convergence for several quantities arising naturally in statistical physics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-24T12:46:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F99",
      "60B12",
      "62E20",
      "60K35"
    ],
    "keywords": [
      "additive functions",
      "glivenko-cantelli theorem",
      "short range correlations",
      "explicit error estimate",
      "yield uniform convergence"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}