Statistical properties for mixing Markov chains with applications to dynamical systems
Dynamical Systems
2025-07-17 v5 Probability
Abstract
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of 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, including systems for which the spectral gap property for the transition or the transfer operator does not hold.
Cite
@article{arxiv.2210.16908,
title = {Statistical properties for mixing Markov chains with applications to dynamical systems},
author = {Ao Cai and Pedro Duarte and Silvius Klein},
journal= {arXiv preprint arXiv:2210.16908},
year = {2025}
}
Comments
44 pages, 1 figure. Compared to the previous version we added several references and expanded the remarks following Theorem 1.1, according to the suggestions of the referee