Continuum percolation for the Boolean model.

Nom de l'orateur
David Dereudre
Etablissement de l'orateur
Lille 1
Date et heure de l'exposé
Lieu de l'exposé
Salle Eole

The Boolean model is defined as a union of balls in $R^d$ where the centers are the points of an homogeneous Poisson point process with intensity $z>0$ and the radii are independent and identically distributed following a law $Q$ on $R^+$. The percolation properties mainly refer to the existence of an unbounded connected component in a random spatial model. In this talk we give classical results for the percolation of the Boolean model. In particular, we will see several phase transition results with respect to the stochastic properties of $Q$ (moments, support, etc). We will discuss conjectures about the critical volumic fraction of percolation.