Discrepancy Skew Products and Affine Random Walks

TL;DR

This paper establishes bounded rational ergodicity for certain discrepancy skew products with poorly approximable rotation numbers by analyzing the asymptotic behavior of related affine random walks.

Contribution

It introduces a novel approach linking discrepancy skew products with affine random walks to prove ergodic properties.

Findings

Bounded rational ergodicity established for specific skew products.

Connection between discrepancy skew products and affine random walks.

Asymptotic analysis used to derive ergodic properties.

Abstract

We prove bounded rational ergodicity for some discrepancy skew products whose rotation number has bad rational approximation. This is done by considering the asymptotics of associated affine random walks.