Abstract
We use a variant of a discrete time exclusion process, studied by Yaguchi [7], to construct a Markov random field which isK but not Bernoulli. Instead of having all the particles in the exclusion process indistinguishable, this system has two different types of particles.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. P. Conze,Entropie d’un groupe abélian de transformations, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete25 (1972), 11–30.
J. Feldman,New K-automorphisms and a problem of Kakutani, Israel Journal of Mathematics24 (1976), 16–38.
N. A. Friedman and D. Ornstein,On isomorphism of weak Bernoulli transformations, Advances in Mathematics5 (1970), 365–394.
F. den Hollander and J. Steif,On K-automorphisms, Bernoulli shifts and Markov random fields, Ergodic Theory and Dynamical Systems, to appear.
F. Ledrappier,Un champ markovien peut être d’entropie nulle et mélangeant, Comptes Rendus de l’Académie des Sciences, Paris287 (1978), A561-A563.
I. Mejilson,Mixing properties of a class of skew-products, Israel Journal of Mathematics19 (1974), 266–270.
H. Yaguchi,Stationary measures for an exclusion process on one-dimensional lattices with infinitely many hopping sites, Hiroshima Mathematical Journal16 (1986), 449–475.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hoffman, C. A markov random field which isK but not Bernoulli. Isr. J. Math. 112, 249–269 (1999). https://doi.org/10.1007/BF02773484
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02773484