A Breiman Type Theorem for Gibbs Measures

For a translation invariant Gibbs measure on a suitable translation invariant configuration set X [sub] S super()G where G is an amenable group and S is a finite set, we prove the convergence of the Shannon-McMillan-Breiman ratio on a specific subset of 'generic' configurations. Provided t...

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Bibliographic Details
Published in:Journal of dynamical and control systems 2007-07, Vol.13 (3), p.363-371
Main Authors: Gurevich, B. M., Tempelman, A. A.
Format: Article
Language:English
Subjects:
Control systems
Convergence
Invariants
Mathematical analysis
Theorems
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Summary:For a translation invariant Gibbs measure on a suitable translation invariant configuration set X [sub] S super()G where G is an amenable group and S is a finite set, we prove the convergence of the Shannon-McMillan-Breiman ratio on a specific subset of 'generic' configurations. Provided that the above Gibbs measure exists, we also prove the convergence in the definition of the pressure and the fact that this Gibbs measure is an equilibrium measure.
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-007-9019-3