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.
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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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Chenavier, N., Nagel, W. The largest order statistics for the inradius in an isotropic STIT tessellation. Extremes 22, 571–598 (2019). https://doi.org/10.1007/s10687-019-00356-0
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DOI: https://doi.org/10.1007/s10687-019-00356-0