Abstract

Let double-struck M sign = ℕD be the positive orthant of a D-dimensional lattice and let (g, +) be a finite abelian group. Let ω ⊆ gdouble-struck M sign be a subgroup shift, and let μ be a Markov random field whose support is &. Let Φ: ω → ω be a linear cellular automaton. Under broad conditions on g, we show that the Cesaro average N-1 ∑n=0 N-1 Φn (μ) converges to a measure of maximal entropy for the shift action on ω. © 2005 Cambridge University Press.