Journal of Statistical Physics

, Volume 143, Issue 4, pp 795–806 | Cite as

Zero Temperature Limits of Gibbs Equilibrium States for Countable Markov Shifts



We prove that, given a uniformly locally constant potential f on a countable state Markov shift and suitable conditions which guarantee the existence of the equilibrium states μ tf for all t, the measures μ tf converge in the weak star topology as t tends to infinity.


Gibbs state Equilibrium state Maximizing measure Countable alphabet Markov shift 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of WarwickCoventryUK

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