{
  "id": "1607.06696",
  "version": "v1",
  "published": "2016-07-22T14:52:26.000Z",
  "updated": "2016-07-22T14:52:26.000Z",
  "title": "A Central Limit Theorem for Lipschitz-Killing Curvatures of Gaussian Excursions",
  "authors": [
    "Dennis Müller"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper studies the excursion set of a real stationary isotropic Gaussian random field above a fixed level. We show that the standardized Lipschitz-Killing curvatures of the intersection of the excursion set with a window converges in distribution to a normal distribution as the window grows to the $d$-dimensional Euclidean space. Moreover a lower bound for the asymptotic variance is shown.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-22T14:52:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60D05",
      "60G60",
      "60G15"
    ],
    "keywords": [
      "central limit theorem",
      "lipschitz-killing curvatures",
      "gaussian excursions",
      "real stationary isotropic gaussian random",
      "stationary isotropic gaussian random field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}