Basic Ideas to Approach Metastability in probabilistic Cellular Automata

Cellular Automata are discrete–time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete time Markov chains on lattice with finite single–cell states whose distinguishing feature is the parallel character of the updating rule. We review the some of the results obtained about the metastable behavior of Probabilistic Cellular Automata and we try to point out difficulties and peculiarities with respect to standard Statistical Mechanics Lattice models.