Asymptotic randomization of subgroup shifts by linear cellular automata

Maass, Alejandro; Martínez, Servet; Pivato, Marcus and Yassawi, Reem (2006). Asymptotic randomization of subgroup shifts by linear cellular automata. Ergodic Theory Dynam. Systems, 26(4) pp. 1203–1224.

DOI: https://doi.org/10.1017/S0143385706000216

Abstract

Let M = N^D be the positive orthant of a D-dimensional lattice and let (G, +) be a finite abelian group. Let G ⊆ GM be a subgroup shift, and let µ be a Markov random field whose support is G. Let � : G−→G be a linear cellular automaton. Under broad conditions on G, we show that the Cesaro average N−1 �N−1 n=0 �n(µ) converges to a measure of maximal entropy for the shift action on G.

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