Abstract
We give conditions for the Bernoullicity of the ν-dimensional Markov processes.
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References
Spitzer, F.: Am. Math. Monthly78, 142 (1971) for a more general formulation see, for instance: Tesei, A.: On the equivalence between Gibbs and Markov processes [preprint (1973)], Roma
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For a definition of 2-dimensionalK-system see: Lanford, O., Ruelle, D.: Commun. math. Phys.13, 194 (1968). For the proof of the statement see the quoted paper by Lanford-Ruelle or R. L. Dobrushin in [2]. Actually it is known that (z, β) is aK-system if z≠e−8β, see: Ruelle, D.: Ann. Phys.69, 364 (1972)
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di Liberto, F., Gallavotti, G. & Russo, L. Markov processes, Bernoulli schemes, and Ising model. Commun.Math. Phys. 33, 259–282 (1973). https://doi.org/10.1007/BF01646740
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DOI: https://doi.org/10.1007/BF01646740