Laws of Large Numbers for a Cellular Automaton
Haiyan Cai, Xiaolong Luo · The Annals of Probability · 1993
We prove laws of large numbers for a cellular automaton in the space $\{0,1,\ldots,p - 1\}^Z$ with $p$ being a prime number. The dynamics $\tau$ of the system are defined by $\tau\eta(x) = \eta(x - 1) + \eta(x + 1) \operatorname{mod} p$ for $\eta \in X$.