Ergodicity for a class of probabilistic cellular automata. (English) Zbl 0743.68100

Ferrari, P. A.

Rev. Mat. Apl. 12, No. 2, 93-102 (1991).

Summary: We study a class of probabilistic cellular automata (PCA) which includes majority vote models, discrete time Glauber dynamics and combinations of these processes with mixing dynamics. We give sufficient conditions for the ergodicity of the processes. The method is based on a graphical representation and the construction of a “generalized dual process”.

MSC:

68Q80	Cellular automata (computational aspects)
60K35	Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

ergodic systems; generalized duality; probabilistic cellular automata; graphical representation