Abstract
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 $\eta \in X$.
Citation
Haiyan Cai. Xiaolong Luo. "Laws of Large Numbers for a Cellular Automaton." Ann. Probab. 21 (3) 1413 - 1426, July, 1993. https://doi.org/10.1214/aop/1176989124
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