ON K-AUTOMORPHISMS, BERNOULLI-SHIFTS AND MARKOV RANDOM-FIELDS

Authors
DENHOLLANDER F STEIF JE
Citation
F. Denhollander et Je. Steif, ON K-AUTOMORPHISMS, BERNOULLI-SHIFTS AND MARKOV RANDOM-FIELDS, Ergodic theory & dynamical systems, 17, 1997, pp. 405-415
Citations number
15
Categorie Soggetti
Mathematics,Mathematics
Journal title
Ergodic theory & dynamical systems → ACNP
ISSN journal
01433857
Volume
17
Year of publication
1997
Part
2
Pages
405 - 415
Database
ISI
SICI code
0143-3857(1997)17:<405:OKBAMR>2.0.ZU;2-O
Abstract
We show that for translation invariant Markov random fields: (1) the K -property implies a trivial full tail; (2) the Bernoulli property impl ies Folner independence. The existence of bilaterally deterministic Be rnoulli shifts tells us that neither result is true without the Markov assumption (even in one dimension). We also show that for general tra nslation invariant random fields: (3) Folner independence implies a tr ivial full tail.