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Journal Articles Advances in Applied Probability Year : 2016

Extremes for the inradius in the Poisson line tessellation

Ross Hemsley
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Abstract

A Poisson line tessellation is observed in the window Wρ := B(0, π −1/2 ρ 1/2), for ρ > 0. With each cell of the tessellation, we associate the inradius, which is the radius of the largest ball contained in the cell. Using Poisson approximation, we compute the limit distributions of the largest and smallest order statistics for the inradii of all cells whose nuclei are contained in Wρ as ρ goes to infinity. We additionally prove that the limit shape of the cells minimising the inradius is a triangle.
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hal-01568858 , version 1 (25-07-2017)

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Nicolas Chenavier, Ross Hemsley. Extremes for the inradius in the Poisson line tessellation. Advances in Applied Probability, 2016, 48 (2), pp.544-573. ⟨hal-01568858⟩
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