Non-noise sensitivity for word hyperbolic groups

TL;DR

This paper demonstrates that non-elementary random walks on word hyperbolic groups with finite first moment are robust against small noise, showing a form of insensitivity in their behavior.

Contribution

It establishes a strong form of non-noise sensitivity for random walks on word hyperbolic groups, a novel result in this area.

Findings

Random walks on hyperbolic groups are noise insensitive for small noise parameters.

The result applies to non-elementary groups with finite first moment.

It advances understanding of stability properties of hyperbolic group random walks.

Abstract

We show that non-elementary random walks on word hyperbolic groups with finite first moment are not noise sensitive in a strong sense for small noise parameters.