Mixing rates for potentials of non-summable variations

Author(s)

Gallesco, Christophe ; Takahashi, Daniel Y.

• Document type: Journal article
• Source: Ergodic Theory and Dynamical Systems; v. N/A, p. 18-pg., 2021-07-16.

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. (AU)

• FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
• Grantee: Oswaldo Baffa Filho
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 17/19876-4 - Asymptotic properties of chains of infinite order
• Grantee: Christophe Frédéric Gallesco
• Support Opportunities: Regular Research Grants