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

Nicolas Chenavier (1) , Werner Nagel (2)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville
2 Fakultät für Mathematik und Informatik [Jena]

A planar stationary and isotropic STIT tessellation at time t > 0 is observed in the window Wρ = 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 Wρ as ρ goes to infinity.

Mots clés: Stochastic Geometry; Random Tessellations; Extreme Values; Poisson Approximation

Domaines: Mathématiques [math]; Probabilités [math.PR]

Nicolas Chenavier, Werner Nagel. The largest order statistics for the inradius in an isotropic STIT tessellation. Extremes, 2019, 22 (4), pp.571-598. ⟨10.1007/s10687-019-00356-0⟩. ⟨hal-02189209⟩