Linear cellular automata, asymptotic randomization, and entropy

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dc.creatorPivato, Marcus
dc.date2002-10-16
dc.date.accessioned2026-07-07T04:52:00Z
dc.date.available2026-07-07T04:52:00Z
dc.descriptionIf 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.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0210241
dc.identifierhttp://arxiv.org/abs/math/0210241
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65311
dc.subjectDynamical Systems
dc.subjectProbability
dc.subject37B15 (primary), 68Q80 (secondary)
dc.titleLinear cellular automata, asymptotic randomization, and entropy
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