The Donsker-Varadhan Action Functional for Probabilistic Cellular Automata

Abstract: 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.