On large deviations for amenable group actions

TL;DR

This paper develops large deviations bounds for actions of countable discrete amenable groups by extending entropy formulas and tiling techniques, generalizing classical results to a broader group setting.

Contribution

It introduces an amenable group version of Katok's entropy formula and applies quasi tiling methods to establish large deviations bounds.

Findings

Established large deviations bounds for amenable group actions.

Generalized classical large deviations results to countable discrete amenable groups.

Extended entropy formulas using quasi tiling techniques.

Abstract

By proving an amenable version of Katok's entropy formula and handling the quasi tiling techniques, we establish large deviations bounds for countable discrete amenable group actions. This generalizes the classical results of Lai-Sang Young.