Subcritical monotone cellular automata - Balister, Paul; Bollobás, Béla; Morris, Robert; Smith, Paul (Random structures & algorithms, 2024)
We study monotone cellular automata (also known as 𝒰‐bootstrap percolation) in ℤd$$ {\mathbb{Z}}^d $$ with random initial configurations. Confirming a conjecture of Balister, Bollobás, Przykucki and Smith, who proved the corresponding result in two dimensions, we show that the critical probability is non‐zero for all subcritical models.