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June 2016 Extremes for the inradius in the Poisson line tessellation
Nicolas Chenavier, Ross Hemsley
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Adv. in Appl. Probab. 48(2): 544-573 (June 2016).

Abstract

A Poisson line tessellation is observed in the window Wρ := B(0, π-1/2ρ1/2) 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 the 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 ∞. We additionally prove that the limit shape of the cells minimising the inradius is a triangle.

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Nicolas Chenavier. Ross Hemsley. "Extremes for the inradius in the Poisson line tessellation." Adv. in Appl. Probab. 48 (2) 544 - 573, June 2016.

Information

Published: June 2016
First available in Project Euclid: 9 June 2016

zbMATH: 1342.60011
MathSciNet: MR3511775

Subjects:
Primary: 60D05, 60G55, 60G70
Secondary: 60F05, 62G32

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 2 • June 2016
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