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The noncommutative Markovian property. (English. Russian original) Zbl 0395.60076
Funct. Anal. Appl. 9, 1-7 (1975); translation from Funkts. Anal. Prilozh. 9, No. 1, 1-8 (1975).

MSC:
60J99 Markov processes
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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References:
[1] R. L. Dobrushin, ”Description of random fields by means of conditional probabilities and their regularity conditions,” Teoriya Veroyat. i Prim.,13, No. 2, 201-229 (1968). · Zbl 0184.40403
[2] E. Nelson, ”Quantum fields and Markov fields,” Proc. Amer. Math. Soc. Summer Conference (1971). · Zbl 0236.73070
[3] H. Araki, ”One-dimensional quantum lattice systems,” Matematika,15, No. 1, 101-113 (1971). · Zbl 0239.46068
[4] D. Ruelle, Statistical Mechanics: Rigorous Results, W. A. Benjamin (1969).
[5] S. Sakai, C*-Algebras and W*-Algebras, Springer-Verlag, Berlin (1971).
[6] R. L. Dobrushin and R. A. Minlos, ”Construction of a one-dimensional quantum field by means of a continuous Markov field,” Funktsional. Analiz i Ego Prilozhen.,7, No. 4, 81-82 (1973). · Zbl 0294.60081
[7] C. Lance, ”Tensor products of C*-algebras,” Proc. Varenna Summer School on C*-Algebras and Applications (1973). · Zbl 0252.46065
[8] S. Kakutani and K. Yoshida, ”Operator theoretical treatment of Markov processes,” Ann. Math.,2, No. 42, 188-228 (1941). · Zbl 0024.32402
[9] R. T. Powers, ”Representation of uniformly hyperfinite algebras and their connection with Neumann rings,” Matematika,13, No. 4, 94-124 (1969).
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