Cellular automata, percolation and dynamical dichotomies
Abstract
Gilman’s dichotomy is a classification of one-dimensional cellular automata based on dynamical behaviour emerging from random initial conditions. We demonstrate that Gilman’s classification between equicontinuity and sensitivity with respect to ergodic measures holds on a countable group if and only if it is locally virtually cyclic. We use percolation theory as a tool for the proof.
Fields of Study & Subjects
Cellular Automata and Applications
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Volume
- 379
- Issue
- 9
- Pages
- 6237–6265
- Publication date
- 23 April 2026
- Language
- EN