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- W2115814444 abstract "If $mathbb{M}$ is a monoid and $mathcal{A}$ is an Abelian group, then $mathcal{A}^{mathbb{M}}$ is a compact Abelian group; a linear cellular automaton (LCA) is a continuous endomorphism $mathfrak{F}:mathcal{A}^{mathbb{M}}longrightarrow mathcal{A}^{mathbb{M}}$ that commutes with all shift maps. If $mathfrak{F}$ is diffusive, and $mu$ is a harmonically mixing (HM) probability measure on $mathcal{A}^{mathbb{M}}$, then the sequence ${mathfrak{F}^N mu}_{N=1}^{infty}$ weak* converges to the Haar measure on $mathcal{A}^{mathbb{M}}$ in density. Fully supported Markov measures on $mathcal{A}^{mathbb{Z}}$ are HM and non-trivial LCA on $mathcal{A}^{(mathbb{Z}^D)}$ are diffusive when $mathcal{A}=mathbb{Z}_{/p}$ is a prime cyclic group.In the present work, we provide sufficient conditions for diffusion of LCA on $mathcal{A}^{(mathbb{Z}^D)}$ when $mathcal{A}=mathbb{Z}_{/n}$ is any cyclic group or when $mathcal{A}=(mathbb{Z}_{/p^r})^J$ (p prime). We also show that any fully supported Markov random field on $mathcal{A}^{(mathbb{Z}^D)}$ is HM (where $mathcal{A}$ is any Abelian group)." @default.
- W2115814444 created "2016-06-24" @default.
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- W2115814444 date "2004-12-01" @default.
- W2115814444 modified "2023-10-18" @default.
- W2115814444 title "Limit measures for affine cellular automata II" @default.
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- W2115814444 doi "https://doi.org/10.1017/s0143385704000288" @default.
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