Mixing rates for potentials of non-summable variations

TL;DR

This paper investigates mixing rates and correlation decay for dynamical systems with non-summable potential variations, providing new bounds and inequalities for cases with square summable variations, and establishing related probabilistic results.

Contribution

It introduces a novel block coupling inequality and derives upper bounds for mixing rates in non-summable variation potentials, extending understanding beyond summable cases.

Findings

Established upper bounds for mixing rates with square summable variations

Developed a new block coupling inequality for dynamics with different histories

Proved a weak invariance principle and a Chernoff-type inequality

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.