Asymptotic randomization of subgroup shifts by linear cellular automata

Abstract

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