  We investigate the low-noise regime of a large class of probabilistic
cellular automata, including the North-East-Center model of Toom. They are
defined as stochastic perturbations of cellular automata belonging to the
category of monotonic binary tessellations and possessing a property of
erosion. We prove, for a set of initial conditions, exponential convergence of
the induced processes toward an extremal invariant measure with a highly
predominant spin value. We also show that this invariant measure presents
exponential decay of correlations in space and in time and is therefore
strongly mixing.
