Noise stability on hyperbolic groups

TL;DR

This paper demonstrates that symmetric random walks on non-elementary hyperbolic groups with certain homomorphisms exhibit noise stability at linear scale, given a finite exponential moment condition.

Contribution

It establishes noise stability results for symmetric random walks on hyperbolic groups under specific homomorphism and moment conditions, expanding understanding of stability in geometric group theory.

Findings

Noise stability at linear scale for hyperbolic groups

Conditions involving non-zero homomorphisms and exponential moments

Extension of stability results to a broad class of hyperbolic groups

Abstract

We show that symmetric random walks on non-elementary hyperbolic groups with non-zero homomorphisms into the reals are noise stable at linear scale under finite exponential moment condition.