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Mixing rates for potentials of non-summable variations

Part of: Ergodic theory Markov processes Topological dynamics Stochastic processes

Published online by Cambridge University Press:  16 July 2021

CHRISTOPHE GALLESCO  and
DANIEL Y. TAKAHASHI
CHRISTOPHE GALLESCO*
Affiliation:
Departmento de Estatística, Instituto de Matemática, Estatística e Ciência de Computação, Universidade de Campinas, Campinas, Brasil
DANIEL Y. TAKAHASHI
Affiliation:
Instituto do Cérebro, Universidade Federal do Rio Grande do Norte, Natal, Brasil (e-mail: [email protected])
*
e-mail: [email protected]
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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.

Keywords

g-measurechains of infinite ordercouplingcentral limit theoremconcentration inequality

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces 37A35: Entropy and other invariants, isomorphism, classification 37B15: Cellular automata
Secondary: 60G07: General theory of processes
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 9 , September 2022 , pp. 2823 - 2840
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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