La forme asymptotique du processus de contact en environnement aléatoire

Olivier Garet (1) , Régine Marchand (1)

1 IECN - Institut Élie Cartan de Nancy

The aim of this article is to prove asymptotic shape theorems for the contact process in stationary random environment. These theorems generalize known results for the classical contact process. In particular, if H_t denotes the set of already occupied sites at time t, we show that for almost every environment, when the contact process survives, the set H_t/t almost surely converges to a compact set that only depends on the law of the environment. We introduce new objects which also simplify the proof of the shape theorem in a deterministic environment.

Mots clés: Random growth; contact process; random environment; subadditive ergodic theorem; shape theorem

Domaines: Probabilités [math.PR]

Olivier Garet, Régine Marchand. La forme asymptotique du processus de contact en environnement aléatoire. 2008. ⟨hal-00292881v2⟩