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07 February 2025
 
  » arxiv » 1109.0062

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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
AbstractWe 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
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