abstract

• We establish a connection between percolation on the Cayley graphs of a group and the dynamical diversity of cellular automata on that group. Specifically, we demonstrate that Gilman%27s dichotomy between equicontinuity and sensitivity with respect to Bernoulli measures holds on a finitely generated group if and only if the group has a trivial percolation threshold. Consequently, we show that a countable group satisfies Gilman%27s dichotomy if and only if it is locally virtually cyclic

publication date

• 2024-01-01

published in

• ArXiv  Journal

keywords

Digital Object Identifier (DOI)

• 10.48550/arXiv.2410.23770

PubMed ID

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