Zero Temperature Limits of Gibbs-Equilibrium States for Countable Alphabet Subshifts of Finite Type

@article{Jenkinson2005ZeroTL,
  title={Zero Temperature Limits of Gibbs-Equilibrium States for Countable Alphabet Subshifts of Finite Type},
  author={Oliver Jenkinson and R. Daniel Mauldin and Mariusz Urbanski},
  journal={Journal of Statistical Physics},
  year={2005},
  volume={119},
  pages={765-776}
}
Let ΣA be a finitely primitive subshift of finite type on a countable alphabet. For appropriate functions f:ΣA → IR, the family of Gibbs-equilibrium states (μtf)t⩾1 for the functions tf is shown to be tight. Any weak*-accumulation point as t→∞ is shown to be a maximizing measure for f. 
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