{
  "id": "1709.06838",
  "version": "v1",
  "published": "2017-09-20T12:52:39.000Z",
  "updated": "2017-09-20T12:52:39.000Z",
  "title": "Higher Order Concentration of Measure",
  "authors": [
    "Sergey G. Bobkov",
    "Friedrich Götze",
    "Holger Sambale"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order $d-1$ for any $d \\in \\mathbb{N}$. The bounds are based on $d$-th order derivatives or difference operators. In particular, we consider deviations of functions of independent random variables and differentiable functions over probability measures satisfying a logarithmic Sobolev inequality, and functions on the unit sphere. Applications include concentration inequalities for $U$-statistics as well as for classes of symmetric functions via polynomial approximations on the sphere (Edgeworth-type expansions).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-20T12:52:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "60F10"
    ],
    "keywords": [
      "higher order concentration",
      "th order derivatives",
      "logarithmic sobolev inequality",
      "independent random variables",
      "measure phenomenon"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}