January 2, 2003Open Access

Existence of Gibbs measures for countable Markov shifts

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Abstract

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. Urbański (2001) who showed that this condition is sufficient.

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Omri Sarig (Thu,) studied this question.

synapsesocial.com/papers/69dbc755387cf70698688ad6 https://doi.org/https://doi.org/10.1090/s0002-9939-03-06927-2

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