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

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

2006-08-09

arxiv.org/abs/math/0608222v1

IMS Lecture Notes--Monograph Series 2006, Vol. 48, 100-108

Mathematics

Dynamical Systems

Published at http://dx.doi.org/10.1214/074921706000000130 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000130

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.

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