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Name: Moritz Otto

Talk Title: Poisson approximation in the Poisson hyperplane mosaic

Abstract: We consider point processes of centers of large cells in the Poisson hyperplane mosaic. As a first result, we shall discuss cells with large inradius in arbitrary dimension and derive a Poisson approximation result for the point process of their centers. Our argument uses an appropriate coupling with a Palm version of this process. In the proof we are facing the difficulty that sets that are arbitrarily far apart from each other can be hit by the same hyperplane. In a second step we will generalize our result to other size functionals (e.g. volume, surface area). Finally we shall discuss implications for the distributions of maximal cells.

This talk is a contributed talk at EVA 2021.