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

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-preser...

Full description

Saved in:
Bibliographic Details
Published inErgodic theory and dynamical systems Vol. 42; no. 9; pp. 2890 - 2922
Main Authors LANTHIER, PAUL, DE LA RUE, THIERRY
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.09.2022
Cambridge University Press (CUP)
Subjects
Algebra
Cellular automata
Classification
Dynamical Systems
Mathematics
Original Article
Probability
Random variables
measure-theoretic factors
filtrations
I-cosiness
37A35
60J05
37B15
cellular automata
Filtrations
Online AccessGet full text

Cover

More Information
Summary: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 we study show that this classification leads to different results.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2021.76