Existence of Gibbs measures for countable Markov shifts

@inproceedings{Sarig2003ExistenceOG,
  title={Existence of Gibbs measures for countable Markov shifts},
  author={Omri Sarig},
  year={2003}
}
We prove that a potential with summable variations and finite pressure on a topologically mixing countable Markov shift has a Gibbs measure iff the transition matrix satisfies the big images and preimages property. This strengthens a result of D. Mauldin and M. Urbanski (2001) who showed that this condition is sufficient. 

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