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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Existence of Gibbs measures for countable Markov shifts


Author: Omri Sarig
Journal: Proc. Amer. Math. Soc. 131 (2003), 1751-1758
MSC (2000): Primary 37A99, 37D35; Secondary 37B10
Published electronically: January 2, 2003
MathSciNet review: 1955261
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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. Urbanski (2001) who showed that this condition is sufficient.


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Additional Information

Omri Sarig
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
Email: sarig@maths.warwick.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06927-2
PII: S 0002-9939(03)06927-2
Keywords: Gibbs measures, countable Markov shifts, thermodynamic formalism
Received by editor(s): October 5, 2001
Published electronically: January 2, 2003
Additional Notes: This work is part of a Tel-Aviv University dissertation.
Communicated by: Michael Handel
Article copyright: © Copyright 2003 American Mathematical Society