Gibbs states for non-irreducible countable Markov shifts

Volume 221 / 2013

Andrei E. Ghenciu, Mario Roy Fundamenta Mathematicae 221 (2013), 231-265 MSC: Primary 37B10; Secondary 37B05, 37C40, 28A80. DOI: 10.4064/fm221-3-3


We study Markov shifts over countable (finite or countably infinite) alphabets, i.e. shifts generated by incidence matrices. In particular, we derive necessary and sufficient conditions for the existence of a Gibbs state for a certain class of infinite Markov shifts. We further establish a characterization of the existence, uniqueness and ergodicity of invariant Gibbs states for this class of shifts. Our results generalize the well-known results for finitely irreducible Markov shifts.


  • Andrei E. GhenciuDepartment of Mathematics
    East Central University
    Ada, OK 74820, U.S.A.
  • Mario RoyDepartment of Mathematics
    Glendon College
    York University
    2275 Bayview Avenue
    Toronto, Canada M4N 3M6

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