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arXiv · 2005.13875

The $\beta$-Delaunay tessellation I: Description of the model and geometry of typical cells

Anna Gusakova·Zakhar Kabluchko·Christoph Thäle
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Abstract

In this paper two new classes of stationary random simplicial tessellations, the so-called $\beta$- and $\beta'$-Delaunay tessellations, are introduced. Their construction is based on a space-time paraboloid hull process and generalizes that of the classical Poisson-Delaunay tessellation. The distribution of volume-power weighted typical cells is explicitly identified, establishing thereby a remarkable connection to the classes of $\beta$- and $\beta'$-polytopes. These representations are used to determine principal characteristics of such cells, including volume moments, expected angle sums and cell intensities.

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Anna Gusakova, Zakhar Kabluchko, Christoph Thäle. 2020-05-28. The $\beta$-Delaunay tessellation I: Description of the model and geometry of typical cells. https://arxiv.org/abs/2005.13875

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