Probabilistic cellular automata. At a Crossroads between stochastic processes and statistical physics

Pierre-Yves Louis (1)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]

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.

Mots clés: stochastic processes; ergodicity; long-time behaviour; Gibbs random fields; random systems with infinitely many interacting components; probabilistic cellular automata; fixed boundary conditions

Domaines: Probabilités [math.PR]; Mathématique discrète [cs.DM]; Complexité [cs.CC]; Mécanique statistique [cond-mat.stat-mech]; Automates cellulaires et gaz sur réseau [nlin.CG]

Pierre-Yves Louis. Probabilistic cellular automata. At a Crossroads between stochastic processes and statistical physics. Revue des Sciences et Technologies de l'Information - Série TSI : Technique et Science Informatiques, 2015, ⟨10.3166/TSI.34.431-461⟩. ⟨hal-01283837⟩