Limit theorems for rank-one Lie groups

TL;DR

This paper studies the asymptotic behavior of averaging operators in actions of simple rank-one Lie groups, providing a detailed formula for their deviations from the known convergence limit.

Contribution

It offers a more precise asymptotic formula for the deviations of averaging operators in rank-one Lie group actions, extending previous convergence results.

Findings

Established a detailed asymptotic deviation formula

Extended known almost everywhere convergence results

Enhanced understanding of operator behavior in Lie group actions

Abstract

We investigate asymptotic behaviour of averaging operators for actions of simple rank-one Lie groups. It was previously known that these averaging operators converge almost everywhere, and we establish a more precise asymptotic formula that describes their deviations from the limit.