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

A planar stationary and isotropic STIT tessellation at time t > 0 is observed in the window W ρ = t − 1 π ρ ⋅ [ − 1 2 , 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 W ρ as ρ goes to infinity.