FKG inequalities in cellular automata and coupled map lattices

✍ Scribed by Igor Mezić

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 650 KB
• Volume: 103
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(96)00281-3

✦ Synopsis

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.