Complementability and maximality in different contexts: ergodic theory, Brownian and poly-adic filtrations

TL;DR

This paper explores the concepts of complementability and maximality across ergodic theory, Brownian, and poly-adic filtrations, highlighting their similarities and differences in various mathematical contexts.

Contribution

It provides a comparative analysis of these notions in three different settings, revealing analogies and distinctions that deepen understanding of their roles.

Findings

Identifies key similarities between the concepts in different contexts

Highlights differences in the application and properties of these notions

Provides insights into the structural aspects of filtrations and automorphisms

Abstract

The notions of complementability and maximality were introduced in 1974 by Ornstein and Weiss in the context of the automorphisms of a probability space, in 2008 by Brossard and Leuridan in the context of the Brownian filtrations, and in 2017 by Leuridan in the context of the poly-adic filtrations indexed by the non-positive integers. We present here some striking analogies and also some differences existing between these three contexts.