Statistical properties for mixing Markov chains with applications to dynamical systems

Abstract

We establish an abstract, effective large deviations type estimate for Markov systems satisfying a weak form of strong mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product encoding a random torus translation, a model we call a mixed random-quasiperiodic dynamical system. This abstract scheme is applicable to many other types of skew product dynamics.Comment: 46 pages, 1 figure. Revised version corrects some minor errors in the statement of the CLT, adds more results, remarks and reference