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

Alejandro Maass·Servet Mart\'{ı}nez·Marcus Pivato·Reem Yassawi
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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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Alejandro Maass, Servet Mart\'{ı}nez, Marcus Pivato, Reem Yassawi. 2006-08-09. Attractiveness of the Haar measure for linear cellular automata on Markov subgroups. https://doi.org/10.1214/074921706000000130

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