Spectral Gap and Transience for Ruelle Operators on Countable Markov Shifts

2009 ◽  
Vol 292 (3) ◽  
pp. 637-666 ◽  
Author(s):  
Van Cyr ◽  
Omri Sarig
Keyword(s):  
Spectral Gap ◽  
Markov Shifts ◽  
Countable Markov Shifts

scholarly journals On the existence of maximizing measures for irreducible countable Markov shifts: a dynamical proof

2013 ◽  
Vol 34 (4) ◽  
pp. 1103-1115 ◽  
Author(s):  
RODRIGO BISSACOT ◽  
RICARDO DOS SANTOS FREIRE
Keyword(s):  
Probability Measure ◽  
Bounded Variation ◽  
Finite Alphabet ◽  
Markov Shift ◽  
Positive Real ◽  
Shift Space ◽  
Markov Shifts ◽  
Maximizing Measure ◽  
Full Shift ◽  
Countable Markov Shifts

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} )\rightarrow \mathbb{R} $ is coercive with bounded variation then there exists a maximizing 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 beyond the finitely primitive case in the general irreducible non-compact setting. It is also noteworthy that our technique works for the full shift over positive real sequences.

scholarly journals Thermodynamic formalism for random countable Markov shifts

2008 ◽  
Vol 22 (1/2, September) ◽  
pp. 131-164 ◽  
Author(s):  
Manuel Stadlbauer ◽  
Yuri Kifer ◽  
Manfred Denker
Keyword(s):  
Thermodynamic Formalism ◽  
Markov Shifts ◽  
Countable Markov Shifts

scholarly journals Infinite DLR measures and volume-type phase transitions on countable Markov shifts

Nonlinearity ◽  
2021 ◽  
Vol 34 (7) ◽  
pp. 4819-4843
Author(s):  
Elmer R Beltrán ◽  
Rodrigo Bissacot ◽  
Eric O Endo
Keyword(s):  
Phase Transitions ◽  
Type Phase ◽  
Markov Shifts ◽  
Countable Markov Shifts
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