{
  "id": "2108.09472",
  "version": "v1",
  "published": "2021-08-21T09:15:53.000Z",
  "updated": "2021-08-21T09:15:53.000Z",
  "title": "The $β$-Delaunay tessellation IV: Mixing properties and central limit theorems",
  "authors": [
    "Anna Gusakova",
    "Zakhar Kabluchko",
    "Christoph Thäle"
  ],
  "categories": [
    "math.PR",
    "math.DS"
  ],
  "abstract": "Various mixing properties of $\\beta$-, $\\beta'$- and Gaussian Delaunay tessellations in $\\mathbb{R}^{d-1}$ are studied. It is shown that these tessellation models are absolutely regular, or $\\beta$-mixing. In the $\\beta$- and the Gaussian case exponential bounds for the absolute regularity coefficients are found. In the $\\beta'$-case these coefficients show a polynomial decay only. In the background are new and strong concentration bounds on the radius of stabilization of the underlying construction. Using a general device for absolutely regular stationary random tessellations, central limit theorems for a number of geometric parameters of $\\beta$- and Gaussian Delaunay tessellations are established. This includes the number of $k$-dimensional faces and the $k$-volume of the $k$-sk",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-21T09:15:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A22",
      "52B11",
      "53C65",
      "60D05",
      "60F05"
    ],
    "keywords": [
      "central limit theorems",
      "mixing properties",
      "gaussian delaunay tessellations",
      "gaussian case exponential bounds",
      "absolutely regular stationary random tessellations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}