Covering the whole space with Poisson random balls

Hermine Biermé (1) , Anne Estrade (1)

1 MAP5 - Mathématiques Appliquées à Paris 5

We consider Poisson random balls models generalizing Boolean models with balls for grains. We investigate necessary and sufficient conditions for covering the whole space with these balls. Our arguments are based on both stochastic geometry and martingale theory. Following the framework of percolation theory, a critical regime is exhibited and bounds for critical intensities are obtained.

Mots clés: percolation; Poisson point process; coverage; random set; Boolean model

Domaines: Probabilités [math.PR]

Hermine Biermé, Anne Estrade. Covering the whole space with Poisson random balls. 2009. ⟨hal-00406965v1⟩