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arXiv · 2106.14823

Extremal behavior of large cells in the Poisson hyperplane mosaic

Moritz Otto
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Abstract

We study the asymptotic behavior of a size-marked point process of centers of large cells in a stationary and isotropic Poisson hyperplane mosaic in dimension $d \ge 2$. The sizes of the cells are measured by their inradius or their $k$th intrinsic volume ($k \ge 2$), for example. We prove a Poisson limit theorem for this process in Kantorovich-Rubinstein distance and thereby generalize a result in Chenavier and Hemsley (2016) in various directions. Our proof is based on a general Poisson process approximation result that extends a theorem in Bobrowski, Schulte and Yogeshwaran (2021).

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Moritz Otto. 2021-06-28. Extremal behavior of large cells in the Poisson hyperplane mosaic. https://arxiv.org/abs/2106.14823

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