Existence of Gibbs measures for countable Markov shifts

Sarig, Omri

doi:10.1090/S0002-9939-03-06927-2

Existence of Gibbs measures for countable Markov shifts
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Proc. Amer. Math. Soc. 131 (2003), 1751-1758 Request permission

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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