The Donsker-Varadhan Action Functional for Probabilistic Cellular Automata

From the perspective of the large deviations theory of occupational measures, the paper considers Probabilistic Cellular Automata (PCA) as Markov chains on infinite dimensional space. It turns out that for a wide range of PCA, the corresponding Donsker-Varadhan action functional yields values other than infinity only on a narrow class of probability measures.