Attractiveness of the Haar measure for linear cellular automata on Markov subgroups
Dynamical Systems
2007-05-23 v1 General Topology
Abstract
For the action of an algebraic cellular automaton on a Markov subgroup, we show that the Ces\`{a}ro 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.
Keywords
Cite
@article{arxiv.math/0608222,
title = {Attractiveness of the Haar measure for linear cellular automata on Markov subgroups},
author = {Alejandro Maass and Servet Mart\'{ı}nez and Marcus Pivato and Reem Yassawi},
journal= {arXiv preprint arXiv:math/0608222},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/074921706000000130 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)