Almost sure invariance principle for random piecewise expanding maps

TL;DR

This paper establishes an almost sure invariance principle for random piecewise expanding maps across multiple dimensions, utilizing advanced martingale methods to extend previous theoretical results.

Contribution

It introduces a fiberwise almost sure invariance principle for random piecewise expanding maps, advancing the understanding of their probabilistic behavior in higher dimensions.

Findings

Proves the almost sure invariance principle for random maps

Extends results to higher-dimensional systems

Uses martingale techniques for the proof

Abstract

We prove a fiberwise almost sure invariance principle for random piecewise expanding transformations in one and higher dimensions using recent developments on martingale techniques.