Large deviations for systems with non-uniform structure

Abstract

We use a weak Gibbs property and a weak form of specification to derive level-2 large deviations principles for symbolic systems equipped with a large class of reference measures. This has applications to a broad class of symbolic systems, including β \beta -shifts, S S -gap shifts, and their factors. A crucial step in our approach is to prove a ‘horseshoe theorem’ for these systems.