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arXiv · 2108.09472

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

Anna Gusakova·Zakhar Kabluchko·Christoph Thäle
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Abstract

Various mixing properties of $β$-, $β'$- and Gaussian Delaunay tessellations in $\mathbb{R}^{d-1}$ 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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Anna Gusakova, Zakhar Kabluchko, Christoph Thäle. 2021-08-21. The $β$-Delaunay tessellation IV: Mixing properties and central limit theorems. https://arxiv.org/abs/2108.09472

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