Uniqueness and statistical properties of the Gibbs state on general one-dimensional lattice systems with Markovian structure

Abstract

Let [Formula: see text] be a compact metric space and [Formula: see text], we consider a set of admissible sequences [Formula: see text] determined by a continuous admissibility function [Formula: see text] and a compact set [Formula: see text]. Given a Lipschitz continuous potential [Formula: see text], we prove uniqueness of the Gibbs state [Formula: see text] and we show that it is a Gibbs–Bowen measure and satisfies a central limit theorem.