The Annals of Probability

Laws of Large Numbers for a Cellular Automaton

Haiyan Cai and Xiaolong Luo

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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 $\eta \in X$.

Article information

Source
Ann. Probab., Volume 21, Number 3 (1993), 1413-1426.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989124

Digital Object Identifier
doi:10.1214/aop/1176989124

Mathematical Reviews number (MathSciNet)
MR1235422

Zentralblatt MATH identifier
0787.60121

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Law of large numbers characteristic function cellular automaton Pascal's triangle $\mod p$

Citation

Cai, Haiyan; Luo, Xiaolong. Laws of Large Numbers for a Cellular Automaton. Ann. Probab. 21 (1993), no. 3, 1413--1426. doi:10.1214/aop/1176989124. https://projecteuclid.org/euclid.aop/1176989124


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