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Vertex number of the typical cell in a tri-directional Poisson line tessellation
Nils Heerten, Janina Hübner, Christoph Thäle · 2023-09-22 · via math.PR updates on arXiv.org

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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