The β-Delaunay tessellation IV: Mixing properties and central limit theorems

Abstract

Various mixing properties of [Formula: see text]-, [Formula: see text]- and Gaussian-Delaunay tessellations in [Formula: see text] are studied. It is shown that these tessellation models are absolutely regular, or [Formula: see text]-mixing. In the [Formula: see text]- and the Gaussian case exponential bounds for the absolute regularity coefficients are found. In the [Formula: see text]-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 [Formula: see text]- and Gaussian-Delaunay tessellations are established. This includes the number of [Formula: see text]-dimensional faces and the [Formula: see text]-volume of the [Formula: see text]-skeleton for [Formula: see text].