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Percolation Theory and the Diversity of Cellular Automata on Groups

Felipe García-Ramos ⟨felipegra@yahoo.com⟩

Abstract:

We will explain a connection between the diversity of cellular automata observable on a given countable group and the percolation threshold associated with the Cayley graphs of such groups.

As a consequence, we show that Gilman’s dichotomy holds for the endomorphism semigroup of a countable group if and only if the group is locally virtually cyclic.

Scheduled for: 2025-03-07 10:40 AM: Felipe Garcia-Ramos in Forbes 2070D

Status: Accepted

Collection: Dynamical Systems

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