Random Balls Model With Dependence

Renan Gobard (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this article, we consider a configuration of weighted random balls in $\mathbb{R}^d$ generated according to a Poisson point process. The model investigated exhibits inhomogeneity, as well as dependence between the centers and the radii and heavy tails phenomena. We investigate the asymptotic behavior of the total mass of the configuration of the balls at a macroscopic level. Three different regimes appear depending on the intensity parameters and the zooming factor. Among the three limiting fields, two are stable while the third one is a Poisson integral bridging between the two stable regimes. For some particular choices of the inhomogeneity function, the limiting fields exhibit isotropy or self-similarity.

Mots clés: Poisson Point Process; generalized random fields; stable fields

Domaines: Probabilités [math.PR]

Renan Gobard. Random Balls Model With Dependence. Journal of Mathematical Analysis and Applications, 2015, 423 (2), pp.1284-1310. ⟨10.1016/j.jmaa.2014.10.055⟩. ⟨hal-01000972⟩