Summary
Two results concerning the local conditional distributions of a stationary measure for a spin flip process with strictly positive and continuous rates are obtained: 1) The local conditional distributions and the rates of the reversed process determine each other. 2) Either all shift invariant stationary measures are Gibbs with the same potential or no shift invariant stationary Gibbs measure exist.
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Research supported by the Japan Society for the Promotion of Science
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Künsch, H. Non reversible stationary measures for infinite interacting particle systems. Z. Wahrscheinlichkeitstheorie verw Gebiete 66, 407–424 (1984). https://doi.org/10.1007/BF00533706
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DOI: https://doi.org/10.1007/BF00533706