Classification of backward filtrations and factor filtrations: examples from cellular automata

@article{Lanthier2021ClassificationOB,
  title={Classification of backward filtrations and factor filtrations: examples from cellular automata},
  author={Paula A. Lanthier and Thierry DE LA RUE},
  journal={Ergodic Theory and Dynamical Systems},
  year={2021},
  volume={42},
  pages={2890 - 2922}
}
Abstract We consider backward filtrations generated by processes coming from deterministic and probabilistic cellular automata. We prove that these filtrations are standard in the classical sense of Vershik’s theory, but we also study them from another point of view that takes into account the measure-preserving action of the shift map, for which each sigma-algebra in the filtrations is invariant. This initiates what we call the dynamical classification of factor filtrations, and the examples… 

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