Deviation and concentration inequalities for dynamical systems with subexponential decay of correlation

TL;DR

This paper derives deviation and concentration inequalities for nonuniformly expanding dynamical systems with stretched exponential decay of correlations, providing essentially optimal bounds in the large deviation regime.

Contribution

It introduces new deviation and concentration inequalities for a class of dynamical systems with subexponential decay, with optimal bounds demonstrated.

Findings

Derived large deviation estimates with optimal bounds

Established concentration inequalities for nonuniformly expanding maps

Provided examples confirming the sharpness of bounds

Abstract

We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples showing that the obtained upper bounds are essentially optimal.