Mixing rates for potentials of non-summable variations
Dynamical Systems
2021-06-17 v3 Probability
Abstract
Mixing rates and decay of correlations for dynamics defined by potentials with summable variations are well understood, but little is known for non-summable variations. In this paper, we exhibit upper bounds for these quantities in the case of dynamics defined by potentials with square summable variations. We obtain these bounds as corollaries of a new block coupling inequality between pair of dynamics starting with different histories. As applications of our results, we prove a new weak invariance principle and a Chernoff-type inequality.
Cite
@article{arxiv.2006.06824,
title = {Mixing rates for potentials of non-summable variations},
author = {Christophe Gallesco and Daniel Y. Takahashi},
journal= {arXiv preprint arXiv:2006.06824},
year = {2021}
}
Comments
20 pages