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Module shifts and measure rigidity in linear cellular automata
Published online by Cambridge University Press: 16 September 2008
Abstract
Suppose ℛ is a finite commutative ring of prime characteristic, 𝒜 is a finite ℛ-module, 𝕄:=ℤD×ℕE, and Φ is an ℛ-linear cellular automaton on 𝒜𝕄. If μ is a Φ-invariant measure which is multiply σ-mixing in a certain way, then we show that μ must be the Haar measure on a coset of some submodule shift of 𝒜𝕄. Under certain conditions, this means that μ must be the uniform Bernoulli measure on 𝒜𝕄.
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- Copyright © 2008 Cambridge University Press
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