Asymptotics of the visibility function in the Boolean model

Pierre Calka (1) , Julien Michel (2) , Sylvain Porret-Blanc (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

The aim of this paper is to give a precise estimate on the tail probability of the visibility function in a germ-grain model: this function is defined as the length of the longest ray starting at the origin that does not intersect an obstacle in a Boolean model. We proceed in two or more dimensions using coverage techniques. Moreover, convergence results involving a type I extreme value distribution are shown in the two particular cases of small obstacles or a large obstacle-free region.

Mots clés: Boolean model; Poisson point process; Coverage processes; Stochastic geometry; Extreme value distribution

Domaines: Probabilités [math.PR]

Pierre Calka, Julien Michel, Sylvain Porret-Blanc. Asymptotics of the visibility function in the Boolean model. 2009. ⟨hal-00389798v1⟩