A rank one mild mixing system without minimal self joinings

March 17, 2026Annales Henri LebesgueOpen Access

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Key Points

This research aims to identify a rank one transformation exhibiting mild mixing properties while lacking minimal self-joinings.
Develop a mathematical framework for analyzing rank one transformations.
Explore properties of mildly mixing systems and their relationship to self-joinings.
Demonstrated the existence of a rank one transformation with mild mixing properties.
Confirmed that this transformation does not possess minimal self-joinings, providing a novel example in the field.

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This research shows a transformation that is mildly mixing without minimal self-joinings, addressing Thouvenot's question.

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.

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Chaika et al. (2026) studied this question.

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