Extremal behavior of large cells in the Poisson hyperplane mosaic

2021/06/28 by Moritz Otto, Otto, Moritz
Computer Science · Mathematics · #60D05 #60F17 #60G55 #Bayesian Methods and Mixture Models #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.2106.14823

openalex publication_date 2021/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ≥ 2. The sizes of the cells are measured by their inradius or their kth intrinsic volume (k ≥ 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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