Automates cellulaires probabilistes et de la physique statistique

Abstract

Probabilistic cellular automata are considered in this review. They are CA dynamics whose updating rule is a probability depending on each site's neighbourhood. Spatial homogeneity is recovered in distribution. Several families of examples are considered. The time-asymptotic behaviour is highly non trivial. Ergodicity and dynamical phase transition phenomena are explained and some associated criteria are given. These stochastic processes dynamics are considered from a statistical mechanics point of view. The relationships between the infinitely-many interacting case and the associated finite-volume case are stated. The importance of fixed boundary condition is emphasised.