Følner Independence and the amenable Ising model

Scot Adams

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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).

Original languageEnglish (US)
Pages (from-to)633-657
Number of pages25
JournalErgodic Theory and Dynamical Systems
Volume12
Issue number4
DOIs
StatePublished - Dec 1992

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