Følner Independence and the amenable Ising model

Scot Adams

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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
Issue number4
StatePublished - Dec 1992


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