FKG INEQUALITIES IN CELLULAR-AUTOMATA AND COUPLED MAP LATTICES

We review conditions for the preservation of the FKG (Fortuin-Kasteley n-Ginibre) inequalities in cellular automata and coupled map lattices. In addition, conditions are derived on the transition probabilities f or N-state probabilistic cellular automata which insure monotonicity a nd preservation of FKG inequalities. This can be used, for example, to prove normal fluctuation and large deviations theorems for these syst ems. A number of examples of probabilistic cellular automata and coupl ed map lattices that preserve positive correlations are presented and the implications of FKG inequalities are discussed.