Følner Independence and the amenable Ising model
1992 ◽
Vol 12
(4)
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pp. 633-657
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AbstractWe 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).
1996 ◽
Vol 84
(5-6)
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pp. 1077-1093
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Keyword(s):
1976 ◽
Vol 48
(3)
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pp. 249-265
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1991 ◽
Vol 90
(2)
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pp. 203-221
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2005 ◽
Vol 135
(2)
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pp. 153-168
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2014 ◽
Vol 334
(1)
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pp. 313-330
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2012 ◽
Vol 148
(6)
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pp. 999-1005
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1992 ◽
Vol 66
(1-2)
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pp. 139-164
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2000 ◽
Vol 123
(1)
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pp. 489-493
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Keyword(s):
1986 ◽
Vol 66
(1)
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pp. 72-80
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