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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About

• Item ORO ID
• 67102
• Item Type
• Book Section
• ISBN
• 0-940600-64-1, 978-0-940600-64-5
• Keywords
• cellular automata; maximal entropy measure; Markov measures; algebraic topological Markov chain
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2006 Institute of Mathematical Statistics
• Depositing User
• Reem Yassawi