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On K-automorphisms, Bernoulli shifts and Markov random fields

Published online by Cambridge University Press:  17 April 2001

FRANK DEN HOLLANDER  and
JEFFREY E. STEIF
FRANK DEN HOLLANDER
Affiliation:
Department of Mathematics, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands (e-mail: denholla@sci.kun.nl)
JEFFREY E. STEIF
Affiliation:
Department of Mathematics, Chalmers University of Technology, S-41296 Gothenburg, Sweden (e-mail: steif@math.chalmers.se)
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Abstract

We show that for translation invariant Markov random fields: (1) the K-property implies a trivial full tail; (2) the Bernoulli property implies Følner independence. The existence of bilaterally deterministic Bernoulli shifts tells us that neither result is true without the Markov assumption (even in one dimension). We also show that for general translation invariant random fields: (3) Følner independence implies a trivial full tail.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 2 , April 1997 , pp. 405 - 415
Copyright
1997 Cambridge University Press

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