Attractiveness of the Haar measure for linear cellular automata on Markov subgroups

Maass, Alejandro; Martínez, Servet; Pivato, Marcus and Yassawi, Reem (2006). Attractiveness of the Haar measure for linear cellular automata on Markov subgroups. In: Denteneer, Dee; den Hollander, Frank and Verbitskiy, Evgeny eds. Dynamics & Stochastics: Festschrift in honor of M. S. Keane. The Institute of Mathematical Statistics Lecture Notes - Monograph Series, 48. Beachwood, Ohio, USA: Institute of Mathematical Statistics, pp. 100–108.

DOI: https://doi.org/10.1214/lnms/1196285812

Abstract

For the action of an algebraic cellular automaton on a Markov subgroup, we show that the Cesàro mean of the iterates of a Markov measure converges to the Haar measure. This is proven by using the combinatorics of the binomial coefficients on the regenerative construction of the Markov measure.

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