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Disjointness for measurably distal group actions and applications
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Moreira, Joel, Richter, Florian K. and Robertson, Donald (2023) Disjointness for measurably distal group actions and applications. Ergodic Theory and Dynamical Systems, 43 (6). pp. 1952-1979. doi:10.1017/etds.2022.19 ISSN 0143-3857.
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Official URL: http://doi.org/10.1017/etds.2022.19
Abstract
We generalize Berg’s notion of quasi-disjointness to actions of countable groups and prove that every measurably distal system is quasi-disjoint from every measure-preserving system. As a corollary, we obtain easy to check necessary and sufficient conditions for two systems to be disjoint, provided one of them is measurably distal. We also obtain a Wiener–Wintner-type theorem for countable amenable groups with distal weights and applications to weighted multiple ergodic averages and multiple recurrence.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Ergodic theory , Measure-preserving transformations , Spectral theory (Mathematics), Markov operators, Entropy | ||||||||||||
| Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||||||||||
| Publisher: | Cambridge University Press | ||||||||||||
| ISSN: | 0143-3857 | ||||||||||||
| Official Date: | June 2023 | ||||||||||||
| Dates: |
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| Volume: | 43 | ||||||||||||
| Number: | 6 | ||||||||||||
| Page Range: | pp. 1952-1979 | ||||||||||||
| DOI: | 10.1017/etds.2022.19 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
| Copyright Holders: | © The Author(s), 2022. Published by Cambridge University Press | ||||||||||||
| Date of first compliant deposit: | 26 May 2022 | ||||||||||||
| Date of first compliant Open Access: | 30 June 2022 | ||||||||||||
| RIOXX Funder/Project Grant: |
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