2005/10/26 by Mathieu Sablik, Sablik, Mathieu · 1 citation
Computer Science · Mathematics · #Advanced Operator Algebra Research #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.math/0510564
openalex publication_date 2005/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (\az,F) be a bipermutative algebraic cellular automaton. We present conditions which force a probability measure which is invariant for the \N×\Z-action of F and the shift map \s to be the Haar measure on \gs, a closed shift-invariant subgroup of the Abelian compact group \az. This generalizes simultaneously results of B. Host, A. Maass and S. Mart'ınez \citeHost-Maass-Martinez-2003 and M. Pivato \citePivato-2003. This result is applied to give conditions which also force a (F,\s)-invariant probability measure to be the uniform Bernoulli measure when F is a particular invertible expansive cellular automaton on \an.