FKG inequalities in cellular automata and coupled map lattices

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

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