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.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Algebra and Number Theory
- Numerical Analysis
- Control and Optimization