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Article overview
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On the existence of maximizing measures for irreducible countable Markov shifts: a dynamical proof | Rodrigo Bissacot
; Ricardo Freire
; | Date: |
1 Sep 2011 | Abstract: | We prove that if $Sigma_{mathbf A}(mathbb N)$ is an irreducible Markov
shift space over $mathbb N$ and $f:Sigma_{mathbf A}(mathbb N)
ightarrow
mathbb R$ is coercive with bounded variation then there exists a maxi-mizing
probability measure for $f$, whose support lies on a Markov subshift over a
finite alphabet. Furthermore, the support of any maximizing measure is
contained in this same compact subshift. To the best of our knowledge, this is
the first proof of the existence of maximizing measures beyond the finitely
primitive case on the non-compact setting. It’s also noteworthy that our
technique works in the case of the full shift over positive real sequences. | Source: | arXiv, 1109.0062 | Services: | Forum | Review | PDF | Favorites |
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