Noise sensitivity of random walks on groups

A random walk on a group is noise sensitive if resampling every step independently with a small probability results in an almost independent output. We precisely define two notions: l(1)-noise sensitivity and entropy noise sensitivity. Groups with one of these properties are necessarily Liouville. Homomorphisms to free abelian groups provide an obstruction to l(1)-noise sensitivity. We also provide examples of l(1) and entropy noise sensitive random walks. Noise sensitivity raises many open questions which are described at the end of the paper.