Linear cellular automata, asymptotic randomization, and entropy
Dynamical Systems
2007-05-23 v1 Probability
Abstract
If A=Z/2, then A^Z is a compact abelian group. A `linear cellular automaton' is a shift-commuting endomorphism F of A^Z. If P is a probability measure on A^Z, then F `asymptotically randomizes' P if F^j P converges to the Haar measure as j-->oo, for j in a subset of Cesaro density one. Via counterexamples, we show that nonzero entropy of P is neither necessary nor sufficient for asymptotic randomization.
Cite
@article{arxiv.math/0210241,
title = {Linear cellular automata, asymptotic randomization, and entropy},
author = {Marcus Pivato},
journal= {arXiv preprint arXiv:math/0210241},
year = {2007}
}
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8 pages