  In this paper, we introduce a noisy framework for SFTs, allowing some amount
of forbidden patterns to appear. Using the Besicovitch distance, which permits
a global comparison of configurations, we then study the closeness of noisy
measures to non-noisy ones as the amount of noise goes to 0. Our first main
result is the full classification of the (in)stability in the one-dimensional
case. Our second main result is a stability property under Bernoulli noise for
higher-dimensional periodic SFTs, which we finally extend to an aperiodic
example through a variant of the Robinson tiling.
