Asymptotic decoupling and weak Gibbs measures for finite alphabet shift spaces

Abstract

For the space X in a large class of finite alphabet shift spaces (lattice models) and the class of functions f with bounded total oscillations, we prove that each equilibrium measure ν at f = φ is a weak Gibbs measures for φ − P(φ). In addition, the empirical measures satisfy a full large deviations principle for (X, ν).