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