Gibbs states for non-irreducible countable Markov shifts

Andrei E. Ghenciu; Mario Roy

Gibbs states for non-irreducible countable Markov shifts

Andrei E. Ghenciu; Mario Roy

Fundamenta Mathematicae (2013)

Volume: 221, Issue: 3, page 231-265
ISSN: 0016-2736

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Abstract

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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.

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Andrei E. Ghenciu, and Mario Roy. "Gibbs states for non-irreducible countable Markov shifts." Fundamenta Mathematicae 221.3 (2013): 231-265. <http://eudml.org/doc/283178>.

@article{AndreiE2013,
abstract = {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.},
author = {Andrei E. Ghenciu, Mario Roy},
journal = {Fundamenta Mathematicae},
keywords = {Gibbs states; countable-state Markov shifts; finitely irreducible; reducible},
language = {eng},
number = {3},
pages = {231-265},
title = {Gibbs states for non-irreducible countable Markov shifts},
url = {http://eudml.org/doc/283178},
volume = {221},
year = {2013},
}

TY - JOUR
AU - Andrei E. Ghenciu
AU - Mario Roy
TI - Gibbs states for non-irreducible countable Markov shifts
JO - Fundamenta Mathematicae
PY - 2013
VL - 221
IS - 3
SP - 231
EP - 265
AB - 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.
LA - eng
KW - Gibbs states; countable-state Markov shifts; finitely irreducible; reducible
UR - http://eudml.org/doc/283178
ER -

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