Specification and towers in shift spaces
Abstract
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 of quasi-finite type, synchronised and coded shifts, and factors of beta-shifts and S-gap shifts.
Cite
@article{arxiv.1502.00931,
title = {Specification and towers in shift spaces},
author = {Vaughn Climenhaga},
journal= {arXiv preprint arXiv:1502.00931},
year = {2018}
}
Comments
62 pages. Theorem 1.2 in the previous version has been split into Theorems 1.2 and 1.3, to separate the process of obtaining a tower representation from its consequences for statistical properties