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On the Global Markov Property

  • Hans Föllmer

Abstract

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”.

Keywords

Gibbs Measure Markov Property Arbitrary Subset High Density State Standard Borel Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag/Wien 1980

Authors and Affiliations

  • Hans Föllmer
    • 1
  1. 1.MathematikdepartementETH-ZentrumZürichSwitzerland

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