Specification and Towers in Shift Spaces

@article{Climenhaga2015SpecificationAT,
  title={Specification and Towers in Shift Spaces},
  author={V. Climenhaga},
  journal={Communications in Mathematical Physics},
  year={2015},
  volume={364},
  pages={441-504}
}
  • V. Climenhaga
  • Published 2015
  • Mathematics
  • Communications in Mathematical Physics
  • We show that a shift space on a finite alphabet with a non-uniform specification property can be modeled by a strongly positive recurrent countable-state Markov shift to which every equilibrium state lifts. In addition to uniqueness of the equilibrium state, this gives strong statistical properties including the Bernoulli property, exponential decay of correlations, central limit theorem, and analyticity of pressure, which are new even for uniform specification. We give applications to shifts… CONTINUE READING
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