Author:
GALLESCO CHRISTOPHE,TAKAHASHI DANIEL Y.
Abstract
Abstract
Mixing rates, relaxation rates, and decay of correlations for dynamics defined by potentials with summable variations are well understood, but little is known for non-summable variations. This paper exhibits upper bounds for these quantities for dynamics defined by potentials with square-summable variations. We obtain these bounds as corollaries of a new block coupling inequality between pairs of dynamics starting with different histories. As applications of our results, we prove a new weak invariance principle and a Hoeffding-type inequality.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Reference29 articles.
1. Countable state shifts and uniqueness of g -measures
2. Sur des chaînes à liaisons complètes
3. On chains of infinite orde
4. Measure concentration for a class of random processes
5. [CGT20] Chazottes, J.-R. , Gallo, S. and Takahashi, D. Y. . Optimal Gaussian concentration bounds for stochastic chains of unbounded memory. Preprint, 2020, arXiv:2001.06633.