Classification of Backward Filtrations and Factor Filtrations: Examples from Cellular Automata

Paul Lanthier (1) , Thierry de La Rue (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

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 measurepreserving 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 we study show that this classification leads to different results.

Mots clés: Filtrations; I-cosiness; measure-theoretic factors; cellular automata

Domaines: Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Paul Lanthier, Thierry de La Rue. Classification of Backward Filtrations and Factor Filtrations: Examples from Cellular Automata. 2021. ⟨hal-03160525v2⟩