A Breiman type theorem for Gibbs measures

B. M. Gurevich; Arkady A. Tempelman

doi:10.1007/s10883-007-9019-3

A Breiman type theorem for Gibbs measures

B. M. Gurevich, Arkady A. Tempelman

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

For a translation invariant Gibbs measure on a suitable translation invariant configuration set X ⊂ S ^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.

Original language	English (US)
Pages (from-to)	363-371
Number of pages	9
Journal	Journal of Dynamical and Control Systems
Volume	13
Issue number	3
DOIs	https://doi.org/10.1007/s10883-007-9019-3
State	Published - Jul 2007

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Algebra and Number Theory
Numerical Analysis
Control and Optimization

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10.1007/s10883-007-9019-3

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note = "Funding Information: The work of the first author is partially supported by the Russian Foundation for Basic Research (project No. 05-00-00449).",

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AU - Tempelman, Arkady A.

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AB - For a translation invariant Gibbs measure on a suitable translation invariant configuration set X ⊂ S 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.

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JO - Journal of Dynamical and Control Systems

JF - Journal of Dynamical and Control Systems

IS - 3

ER -

A Breiman type theorem for Gibbs measures

Abstract

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