{
  "id": "1706.06985",
  "version": "v1",
  "published": "2017-06-21T16:17:22.000Z",
  "updated": "2017-06-21T16:17:22.000Z",
  "title": "An Improved Second Order Poincaré Inequality for Functionals of Gaussian Fields",
  "authors": [
    "Anna Vidotto"
  ],
  "comment": "50 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We present an improved version of the second order Gaussian Poincar\\'e inequality, developed in Chatterjee (2009) and Nourdin, Peccati and Reinert (2009), which we use in order to bound distributional distances between functionals of Gaussian fields and a normal random variable. Some applications are developed, including a quantitative version of the Sinai-Soshnikov CLT and the Breuer-Major theorems, improving some previous findings in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-21T16:17:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian fields",
      "functionals",
      "second order gaussian poincare inequality",
      "bound distributional distances",
      "breuer-major theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}