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

Extremal behavior of large cells in the Poisson hyperplane mosaic