2022/03/25 by Balister, Paul, Bollobás, Béla, Morris, Robert +1
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
paper · doi:10.48550/arxiv.2203.13806
In this paper we study monotone cellular automata in d dimensions. We develop a general method for bounding the growth of the infected set when the initial configuration is chosen randomly, and then use this method to prove a lower bound on the critical probability for percolation that is sharp up to a constant factor in the exponent for every 'critical' model. This is one of three papers that together confirm the Universality Conjecture of Bollobás, Duminil-Copin, Morris and Smith.