Probabilistic cellular automata, invariant measures, and perfect sampling

Ana Busic, Jean Mairesse & Irene Marcovici
In a probabilistic cellular automaton (PCA), the cells are updated synchronously and independently, according to a distribution depending on a finite neighborhood. A PCA can be viewed as a Markov chain whose ergodicity is investigated. A classical cellular automaton (CA) is a particular case of PCA. For a 1-dimensional CA, we prove that ergodicity is equivalent to nilpotency, and is therefore undecidable. We then propose an efficient perfect sampling algorithm for the invariant measure of...