Ergodic Theory and Dynamical Systems
- Ergodic Theory and Dynamical Systems / Volume 12 / Issue 04 / December 1992, pp 633-657
- Copyright © Cambridge University Press 1992
- DOI: http://dx.doi.org/10.1017/S0143385700006994 (About DOI), Published online: 19 September 2008
Research Article
Følner Independence and the amenable Ising model
Scot Adamsa1
a1 Department of Mathematics, Stanford University, Stanford, CA 94305, USA
Abstract
We define a criterion called Følner Independence for a stationary process over an amenable group. Intuitively, a process satisfies the criterion if, for sufficiently invariant Følner sets, the process in the Følner set is nearly independent of the process outside. We show that Følner Independence implies Finitely Determined. As an application, we show that, in its extreme Gibbs states, the amenable attractive Ising model is Følner Independent (hence Finitely Determined, hence Bernoulli).
(Received August 08 1990)
