{
  "id": "1803.05190",
  "version": "v1",
  "published": "2018-03-14T10:20:17.000Z",
  "updated": "2018-03-14T10:20:17.000Z",
  "title": "Higher order concentration in presence of Poincaré-type inequalities",
  "authors": [
    "Friedrich Götze",
    "Holger Sambale"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We show sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order $d-1$ for any $d \\in \\mathbb{N}$. Here we focus on differentiable functions on the Euclidean space in presence of a Poincar\\'e-type inequality. The bounds are based on $d$-th order derivatives.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-14T10:20:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "60F10",
      "60B20"
    ],
    "keywords": [
      "higher order concentration",
      "poincaré-type inequalities",
      "th order derivatives",
      "euclidean space",
      "poincare-type inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}