Subcritical bootstrap percolation via Toom contours

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 relies on recent extension classical framework Toom. This approach is not only simpler than original multi-scale renormalisation result two and more dimensions, but also gives significantly better bounds. As byproduct, improve best known bounds for stability threshold Toom’s North-East-Center majority rule cellular automaton.