The $\beta$-Delaunay tessellation IV: Mixing properties and central limit theorems
Probability
2021-08-24 v1 Dynamical Systems
Abstract
Various mixing properties of -, - and Gaussian Delaunay tessellations in are studied. It is shown that these tessellation models are absolutely regular, or -mixing. In the - and the Gaussian case exponential bounds for the absolute regularity coefficients are found. In the -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 - and Gaussian Delaunay tessellations are established. This includes the number of -dimensional faces and the -volume of the -sk
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Cite
@article{arxiv.2108.09472,
title = {The $\beta$-Delaunay tessellation IV: Mixing properties and central limit theorems},
author = {Anna Gusakova and Zakhar Kabluchko and Christoph Thäle},
journal= {arXiv preprint arXiv:2108.09472},
year = {2021}
}