Self-joinings and generic extensions of ergodic systems

TL;DR

This paper investigates how typical extensions of ergodic systems preserve the property of having trivial pairwise independent self-joinings, connecting to multiple mixing and joining theory.

Contribution

It demonstrates that typical extensions inherit trivial self-joinings, advancing understanding of ergodic system extensions and their mixing properties.

Findings

Extensions inherit trivial self-joinings

Links to multiple mixing problem

Addresses questions in joining theory

Abstract

We show that typical extensions of ergodic systems inherit the triviality of pairwise independent self-joinings. This property (introduced by A. del Junco and D. Rudolph) is related with Rokhlin's famous multiple mixing problem and several questions from joining theory.