Spectral metric spaces for Gibbs measures

Details Spectral metric spaces for Gibbs measures Spectral metric spaces for Gibbs measures

2010-12-23

arxiv.org/abs/1012.5152v2

Mathematics

Operator Algebras

25 pages

Scientific paper

We construct spectral metric spaces for Gibbs measures on a one-sided topologically exact subshift of finite type. That is, for a given Gibbs measure we construct a spectral triple and show that Connes' corresponding pseudo-metric is a metric and that its metric topology agrees with the weak-*-topology on the state space over the set of continuous functions defined on the subshift. Moreover, we show that each Gibbs measure can be fully recovered from the noncommutative integration theory and that the noncommutative volume constant of the associated spectral triple is equal to the reciprocal of the measure theoretical entropy of the shift invariant Gibbs measure.

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