On the Global Markov Property
In a lattice model with nearest neighbor interaction, the Gibbs measures P have the local but not necessarily the global Markov property. We show that the global Markov property does hold in the following two cases: (1) The interaction satisfies Dobrushin’s unigueness condition, or (2) the interaction is attractive, and P is a “high density State”.
KeywordsGibbs Measure Markov Property Arbitrary Subset High Density State Standard Borel Space
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