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Extremes

, Volume 22, Issue 4, pp 571–598 | Cite as

The largest order statistics for the inradius in an isotropic STIT tessellation

  • Nicolas ChenavierEmail author
  • Werner Nagel
Article
  • 19 Downloads

Abstract

A planar stationary and isotropic STIT tessellation at time t > 0 is observed in the window \(W_{\rho }={t^{-1}}\sqrt {\pi \ \rho }\cdot [-\frac {1}{2},\frac {1}{2}]^{2}\), for ρ > 0. With each cell of the tessellation, we associate the inradius, which is the radius of the largest disk contained in the cell. Using the Chen-Stein method, we compute the limit distributions of the largest order statistics for the inradii of all cells whose nuclei are contained in Wρ as ρ goes to infinity.

Keywords

Stochastic geometry Random tessellations Extreme values Poisson approximation 

AMS 2000 Subject Classifications

60D05 60G70 60F05 62G32 

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Notes

Acknowledgments

This work was partially supported by the French ANR grant ASPAG (ANR-17-CE40-0017). The authors thank the referees for their helpful comments.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Université du Littoral Côte d’OpaleLMPA Joseph LiouvilleCalais CedexFrance
  2. 2.Fakultät für Mathematik und InformatikFriedrich-Schiller-Universität JenaJenaGermany

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