Automates cellulaires probabilistes et mesures spécifiques sur des espaces symboliques

摘要: A probabilistic cellular automaton (PCA) is a Markov chain on symbolic space. Time discrete, cells evolve synchronously, and the new content of each cell randomly chosen, independently others, according to distribution given by states in finite neighbourhood cell. PCA are used as computational models computer science, also modelling tool life sciences physics. Moreover, they appear different contexts probability theory combinatorics. ergodic if it has unique attractive invariant measure. We prove that for deterministic CA, ergodicity equivalent nilpotency. This provides proof undecidable. While measure an CA trivial, can be very complex. describe algorithm perfectly sample this certain cases. focus specific families PCA, having Bernoulli or measures, we study properties their space-time diagrams. solve density classification problem infinite lattices dimension greater than equal 2 trees. Finally, problems. give combinatorial characterisation limit measures random walks free products groups. maximal entropy subshift type. play again role last work.