Moment bounds and concentration inequalities for slowly mixing dynamical systems

TL;DR

This paper establishes optimal bounds and inequalities for sums in slowly mixing dynamical systems, including those with anomalous diffusion, advancing understanding of their statistical properties.

Contribution

It provides the first optimal moment bounds and concentration inequalities for a broad class of slowly mixing dynamical systems, including anomalous diffusion cases.

Findings

Optimal moment bounds for Birkhoff sums.

Optimal concentration inequalities for slowly mixing systems.

Applicability to systems with anomalous diffusion.

Abstract

We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit theorem with nonstandard scaling $(n\log n)^{1/2}$.