Open Access
VOL. 48 | 2006 Attractiveness of the Haar measure for linear cellular automata on Markov subgroups
Alejandro Maass, Servet Martínez, Marcus Pivato, Reem Yassawi

Editor(s) Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy

IMS Lecture Notes Monogr. Ser., 2006: 100-108 (2006) DOI: 10.1214/074921706000000130


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.


Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1121.37017
MathSciNet: MR2306192

Digital Object Identifier: 10.1214/074921706000000130

Primary: 54H20‎
Secondary: 37B20

Keywords: algebraic topological Markov chain , cellular automata , Markov measures , maximal entropy measure

Rights: Copyright © 2006, Institute of Mathematical Statistics

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