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

2021/08/21 by Gusakova, Anna, Kabluchko, Zakhar, Thäle, Christoph
#52A22 #52B11 #53C65 #60D05 #60F05 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2108.09472

Abstract

Various mixing properties of β-, β'- and Gaussian Delaunay tessellations in ℝ^d-1 are studied. It is shown that these tessellation models are absolutely regular, or β-mixing. In the β- and the Gaussian case exponential bounds for the absolute regularity coefficients are found. In the β'-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 β- and Gaussian Delaunay tessellations are established. This includes the number of k-dimensional faces and the k-volume of the k-sk

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