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arXiv · 0707.1408

Module Shifts and Measure Rigidity in Linear Cellular Automata

Marcus Pivato
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Abstract

Suppose R is a finite commutative ring of prime characteristic, A is a finite R-module, M:=Z^D x N^E, and F is an R-linear cellular automaton on A^M. If mu is an F-invariant measure which is multiply shift-mixing in a certain way, then we show that mu must be the Haar measure on a coset of some submodule shift of A^M. Under certain conditions, this means mu must be the uniform Bernoulli measure on A^M.

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Marcus Pivato. 2007-07-10. Module Shifts and Measure Rigidity in Linear Cellular Automata. https://arxiv.org/abs/0707.1408

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