  Ergodicity of probabilistic cellular automata is a very important issue in
the PCA theory. In particular, the question about the ergodicity of all PCA
with two-size neighbourhood, two letters alphabet and positive rates is still
open. In this article, we do not try to improve this issue, but we show a new
kind of proof (to the best knowledge of the author) about the ergodicity of
some of those PCA, including also some CA with errors. The proof is based on
the study of the boundaries of islands where the PCA is totally decorrelated
from its initial condition. The behaviours of these boundaries are the ones of
random walks.
