  In this note we provide an alternative proof of the fact that subcritical
bootstrap percolation models have a positive critical probability in any
dimension. The proof relies on a recent extension of the classical framework of
Toom. This approach is not only simpler than the original multi-scale
renormalisation proof of the result in two and more dimensions, but also gives
significantly better bounds. As a byproduct, we improve the best known bounds
for the stability threshold of Toom's North-East-Center majority rule cellular
automaton.

Probability;Combinatorics