Vertex number of the typical cell in a tri-directional Poisson line tessellation

Nils Heerten; Janina Hübner; Christoph Thäle

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arXiv · 2309.12771

Vertex number of the typical cell in a tri-directional Poisson line tessellation

Nils Heerten·Janina Hübner·Christoph Thäle

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Abstract

This paper deals with the typical cell in a Poisson line tessellation in the plane whose directional distribution is concentrated on three equally spread values with possibly different weights. Such a random polygon can only be a triangle, a quadrilateral, a pentagon or a hexagon. The probability for each of these cases is determined explicitly in terms of the weights. Extremal cases are discussed as well.

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Nils Heerten, Janina Hübner, Christoph Thäle. 2023-09-22. Vertex number of the typical cell in a tri-directional Poisson line tessellation. https://arxiv.org/abs/2309.12771

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