Corpus ID: 232147990

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

@inproceedings{Lanthier2021ClassificationOB,
title={Classification of Backward Filtrations and Factor Filtrations: Examples from Cellular Automata},
author={P. Lanthier and T. D. L. Rue},
year={2021}
}
• Published 2021
• Mathematics
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… Expand

#### References

SHOWING 1-10 OF 20 REFERENCES
The theory of decreasing sequences of measurable partitions
• St. Petersbg. Math. J
• 1994
Sufficient conditions for the filtration of a stationary processes to be standard
• Mathematics
• 2017
Let X be a stationary process with values in some $$\sigma$$σ-finite measured state space $$(E,{\mathcal {E}},\pi )$$(E,E,π), indexed by $${{\mathbb {Z}}}$$Z. Call $${{\mathcal {F}}}^X$$FX itsExpand
Ergodicity of Noisy Cellular Automata: The Coupling Method and Beyond
This work presents extensions of the coupling method to small noises when the cellular automaton has some specific properties (hardcore exclusion, nilpotency, permutivity), and proves ergodicity for a small noise. Expand
On Standardness and I-cosiness
The object of study of this work is the invariant characteristics of filtrations in discrete, negative time, pioneered by Vershik. We prove the equivalence between I-cosiness and standardness withoutExpand
On standardness and I-cosiness., Séminaire de Probabilités XLIII, Poitiers, France
• Juin 2009., Berlin: Springer,
• 2011
STATIONARY PROCESSES WHOSE FILTRATIONS ARE STANDARD
• Mathematics
• 2006
We study the standard property of the natural filtration associated to a 0-1 valued stationary process. In our main result we show that if the process has summable memory decay, then the associatedExpand
An introduction to joinings in ergodic theory
Since their introduction by Furstenberg [3], joinings have proved a very powerful tool in ergodic theory. We present here some aspects of the use of joinings in the study of measurable dynamicalExpand
Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• H. Furstenberg
• Mathematics, Computer Science
• Mathematical systems theory
• 2005
The objects of ergodic theory -measure spaces with measure-preserving transformation groups- will be called processes, those of topological dynamics-compact metric spaces with groups of homeomorphisms-will be called flows, and what may be termed the "arithmetic" of these classes of objects is concerned. Expand
A ZERO ENTROPY T SUCH THAT THE [T ,ID] ENDOMORPHISM IS NONSTANDARD
We present an example of an ergodic transformation T , a variant of a zero entropy non loosely Bernoulli map of Feldman [1], such that the sequence of random variables generated by the [T ,Id]Expand