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

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 $\rho >0$. 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 $W_{\rho }$ as $\rho$ goes to infinity.

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