Decomposition of multicorrelation sequences and joint ergodicity

We show that, under finitely many ergodicity assumptions, any multicorrelation sequence defined by invertible measure-preserving $\mathbb {Z}^d$ -actions with multivariable integer polynomial iterates is the sum of a nilsequence and a nullsequence, extending a recent result of the second author. To...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2024-02, Vol.44 (2), p.432-480
Main Authors: DONOSO, SEBASTIÁN, FERRÉ MORAGUES, ANDREU, KOUTSOGIANNIS, ANDREAS, SUN, WENBO
Format: Article
Language:English
Subjects:
Commuting
Decomposition
Ergodic processes
Original Article
Polynomials
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Summary:We show that, under finitely many ergodicity assumptions, any multicorrelation sequence defined by invertible measure-preserving $\mathbb {Z}^d$ -actions with multivariable integer polynomial iterates is the sum of a nilsequence and a nullsequence, extending a recent result of the second author. To this end, we develop a new seminorm bound estimate for multiple averages by improving the results in a previous work of the first, third, and fourth authors. We also use this approach to obtain new criteria for joint ergodicity of multiple averages with multivariable polynomial iterates on ${\mathbb Z}^{d}$ -systems.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2023.30