TY - JOUR
T1 - Følner Independence and the amenable Ising model
AU - Adams, Scot
PY - 1992/12
Y1 - 1992/12
N2 - 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).
AB - 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).
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U2 - 10.1017/S0143385700006994
DO - 10.1017/S0143385700006994
M3 - Article
AN - SCOPUS:84971954869
SN - 0143-3857
VL - 12
SP - 633
EP - 657
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 4
ER -