2002/10/16 by Marcus Pivato, Pivato, Marcus
Mathematics · #37B15 (primary) #68Q80 (secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #math.DS #math.PR #msc:37B15 #msc:68Q80
paper · pdf · doi:10.48550/arxiv.math/0210241
8 pages
arxiv created 2002/10/16 · arxiv updated 2009/11/30
If A=Z/2, then AZ is a compact abelian group. A `linear cellular automaton' is a shift-commuting endomorphism F of AZ. If P is a probability measure on AZ, then F `asymptotically randomizes' P if Fj 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.