A rank one mild mixing system without minimal self joinings

TL;DR

This paper constructs a specific rank one transformation that exhibits mild mixing properties without having minimal self-joinings, addressing a question posed by Thouvenot.

Contribution

It provides the first example of a rank one mild mixing system lacking minimal self-joinings, advancing understanding of mixing properties in ergodic theory.

Findings

Existence of a rank one mildly mixing system without minimal self-joinings

Answers a longstanding open question in ergodic theory

Expands the class of known mixing systems with specific properties

Abstract

We show that there is a rank 1 transformation that is mildly mixing but does not have minimal self-joinings, answering a question of Thouvenot.