Non-Singular $\Z^d$ actions: an ergodic theorem over rectangles with applications to critical dimension

Dooley, A; Jarrett, K

Non-Singular $\Z^d$ actions: an ergodic theorem over rectangles with applications to critical dimension

Dooley, A

Jarrett, K

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Publisher:: Cambridge University Press
Publication Type:: Journal Article
Citation:: Ergodic Theory and Dynamical Systems, 2021, 41, (12), pp. 3722-3739
Issue Date:: 2021-12-01

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Field	Value	Language
dc.contributor.author	Dooley, A https://orcid.org/0000-0002-2656-3042
dc.contributor.author	Jarrett, K
dc.date.accessioned	2022-06-22T00:43:51Z
dc.date.available	2022-06-22T00:43:51Z
dc.date.issued	2021-12-01
dc.identifier.citation	Ergodic Theory and Dynamical Systems, 2021, 41, (12), pp. 3722-3739
dc.identifier.issn	0143-3857
dc.identifier.issn	1469-4417
dc.identifier.uri	http://hdl.handle.net/10453/158304
dc.description.abstract	We adapt techniques developed by Hochman to prove a non-singular ergodic theorem for -actions where the sums are over rectangles with side lengths increasing at arbitrary rates, and in particular are not necessarily balls of a norm. This result is applied to show that the critical dimensions with respect to sequences of such rectangles are invariants of metric isomorphism. These invariants are calculated for the natural action of on a product of d measure spaces.
dc.language	en
dc.publisher	Cambridge University Press
dc.relation.ispartof	Ergodic Theory and Dynamical Systems
dc.relation.isbasedon	10.1017/etds.2020.116
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	0101 Pure Mathematics, 0102 Applied Mathematics, 0802 Computation Theory and Mathematics
dc.subject.classification	General Mathematics
dc.title	Non-Singular $\Z^d$ actions: an ergodic theorem over rectangles with applications to critical dimension
dc.type	Journal Article
utslib.citation.volume	41
utslib.for	0101 Pure Mathematics
utslib.for	0102 Applied Mathematics
utslib.for	0802 Computation Theory and Mathematics
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access	*
pubs.consider-herdc	false
dc.date.updated	2022-06-22T00:43:50Z
pubs.issue	12
pubs.publication-status	Published
pubs.volume	41
utslib.citation.issue	12

Abstract:

We adapt techniques developed by Hochman to prove a non-singular ergodic theorem for -actions where the sums are over rectangles with side lengths increasing at arbitrary rates, and in particular are not necessarily balls of a norm. This result is applied to show that the critical dimensions with respect to sequences of such rectangles are invariants of metric isomorphism. These invariants are calculated for the natural action of on a product of d measure spaces.

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http://hdl.handle.net/10453/158304