{
  "id": "1404.0962",
  "version": "v2",
  "published": "2014-04-03T15:17:28.000Z",
  "updated": "2014-10-01T13:01:31.000Z",
  "title": "Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences",
  "authors": [
    "Kai Krokowski",
    "Anselm Reichenbachs",
    "Christoph Thaele"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Berry-Esseen bounds for non-linear functionals of infinite Rademacher sequences are derived by means of the Malliavin-Stein method. Moreover, multivariate extensions for vectors of Rademacher functionals are shown. The results establish a connection to small-ball probabilities and shed new light onto the relation between central limit theorems on the Rademacher chaos and norms of contraction operators. Applications concern infinite weighted 2-runs, a combinatorial central limit theorem and traces of Bernoulli random matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-03T15:17:28.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-01T13:01:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G50",
      "60B20",
      "60H07"
    ],
    "keywords": [
      "multivariate limit theorems",
      "berry-esseen bounds",
      "functionals",
      "combinatorial central limit theorem",
      "bernoulli random matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.0962K"
    }
  }
}