Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-14T16:33:22.656Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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. Theexistence of bilaterally deterministic Bernoulli shifts tells usthat neither result is true without the Markov assumption (even inone dimension). We also show that for general translationinvariant random fields:(3) Følner independence implies a trivial full tail.

Information

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