2022/03/03 by Paul Balister, Béla Bollobás, Balister, Paul +5 · 1 citation
Computer Science · Mathematics · #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #math.CO #math.PR
paper · pdf · doi:10.48550/arxiv.2203.01917
23 pages, 2 figures, added Theorem 7.1
openalex publication_date 2022/03/03 · arxiv created 2022/04/19 · arxiv updated 2022/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study monotone cellular automata (also known as U-bootstrap percolation) in ℤd 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.