On the Vere–Jones classification and existence of maximal measures for countable topological Markov chains

By Sylvie Ruette. 2003

48 citations recorded by the source corpus.

We consider topological Markov chains (also called Markov shifts) on countable graphs. We show that a transient graph can be extended to a recurrent graph of equal entropy which is either positive recurrent of null recurrent, and we give an example of each type. We extend the notion of local entropy to topological Markov chains and prove that a transitive Markov chain admits a measure of maximal entropy (or maximal measure) whenever its local entropy is less than its (global) entropy.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e7fad8b54d3224e34431b0590767521f7bcf181b

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In Computational Theory and Mathematics

1. Mike Boyle
2. Ricardo Gómez
3. O. Sarig
4. Van Cyr
5. Jérôme Buzzi

In Mathematical Physics

1. Jérôme Buzzi
2. Van Cyr
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7. Vilton Pinheiro
8. Ian Melbourne

Citations in the corpus

• Spectral Gap and Transience for Ruelle Operators on Countable Markov Shifts (2009, result): “The result should be compared with the results of S. Ruette [ Rt ] on the transience of 0.”
• Almost isomorphism for countable state Markov shifts (2004, methodology): “For more background, see [25, 32, 46] and their references for Markov shifts and nonnegative matrices; [65] for entropy and ergodic theory; and [32, 36] for symbolic dynamics.”