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010 a| 2023031263;

020 a| 9781470465483q| (paperback);

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100 1 a| Candela, Pablo.?| UNAUTHORIZED;

245 10 a| Nilspace factors for general uniformity seminorms, cubic exchangeability and limitsh| [electronic resource] /c| Pablo Candela, Balazs Szegedy.;

260 a| Providence, RI :b| American Mathematical Society,c| 2023.;

300 a| v, 101 pages :b| illustrations ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| volume 287, number 1425;

504 a| Includes bibliographical references (pages 99-101).;

505 0 a| Measure-theoretic preliminaries -- Cubic couplings -- The structure theorem for cubic couplings -- On characteristic factors associated with nilpotent group actions -- On cubic exchangeability -- Limits of functions on compact nilspaces.;

506 a| Available only to authorized users.;

520 a| "We study a class of measure-theoretic objects that we call cubic couplings, on which there is a common generalization of the Gowers norms and the Host- Kra seminorms. Our main result yields a complete structural description of cubic couplings, using nilspaces. We give three applications. Firstly, we describe the characteristic factors of Host-Kra type seminorms for measure-preserving actions of countable nilpotent groups. This yields an extension of the structure theorem of Host and Kra. Secondly, we characterize sequences of random variables with a property that we call cubic exchangeability. These are sequences indexed by the infinite discrete cube, such that for every integer k [geq] 0 the joint distribution's marginals on affine subcubes of dimension k are all equal. In particular, our result gives a description, in terms of compact nilspaces, of a related exchangeability property considered by Austin, inspired by a problem of Aldous. Finally, using nilspaces we obtain limit objects for sequences of functions on compact abelian groups (more generally on compact nilspaces) such that the densities of certain patterns in these functions converge. The paper thus proposes a measure-theoretic framework on which the area of higher-order Fourier analysis can be based, and which yields new applications of this area in a unified way in ergodic theory and arithmetic combinatorics"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Nilpotent groups.=| ^A361498;

650 0 a| Curves, Cubic.=| ^A278636;

650 0 a| Ergodic theory.=| ^A15765;

650 0 a| Measure-preserving transformations.=| ^A138854;

650 7 a| Dynamical systems and ergodic theory -- Ergodic theory.2| msc;

650 7 a| Dynamical systems and ergodic theory -- Ergodic theory -- General groups of measure-preserving transformations.2| msc;

650 7 a| Probability theory and stochastic processes.2| msc;

650 7 a| Probability theory and stochastic processes -- Probability theory on algebraic and topological structures.2| msc;

650 7 a| Number theory -- Sequences and sets -- Arithmetic combinatorics; higher degree uniformity.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Szegedy, Balazs.?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30671912;

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Nilspace factors for general uniformity seminorms, cubic exchangeability and limits / Pablo Candela, Balazs Szegedy.

Author/creator	Candela, Pablo
Other author	Szegedy, Balazs.
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2023.
Description	v, 101 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Nilpotent groups. Curves, Cubic. Ergodic theory. Measure-preserving transformations.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; volume 287, number 1425
Contents	Measure-theoretic preliminaries -- Cubic couplings -- The structure theorem for cubic couplings -- On characteristic factors associated with nilpotent group actions -- On cubic exchangeability -- Limits of functions on compact nilspaces.
Abstract	"We study a class of measure-theoretic objects that we call cubic couplings, on which there is a common generalization of the Gowers norms and the Host- Kra seminorms. Our main result yields a complete structural description of cubic couplings, using nilspaces. We give three applications. Firstly, we describe the characteristic factors of Host-Kra type seminorms for measure-preserving actions of countable nilpotent groups. This yields an extension of the structure theorem of Host and Kra. Secondly, we characterize sequences of random variables with a property that we call cubic exchangeability. These are sequences indexed by the infinite discrete cube, such that for every integer k [geq] 0 the joint distribution's marginals on affine subcubes of dimension k are all equal. In particular, our result gives a description, in terms of compact nilspaces, of a related exchangeability property considered by Austin, inspired by a problem of Aldous. Finally, using nilspaces we obtain limit objects for sequences of functions on compact abelian groups (more generally on compact nilspaces) such that the densities of certain patterns in these functions converge. The paper thus proposes a measure-theoretic framework on which the area of higher-order Fourier analysis can be based, and which yields new applications of this area in a unified way in ergodic theory and arithmetic combinatorics"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 99-101).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2023031263
ISBN	9781470465483 (paperback)
ISBN	(pdf)

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Nilspace factors for general uniformity seminorms, cubic exchangeability and limits / Pablo Candela, Balazs Szegedy.

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