Asymptotically Dense Dilations of Sets on the Circle

Daniel Berend; Yuval Peres; Yuval Peres

doi:10.1112/jlms/s2-47.1.1

Asymptotically Dense Dilations of Sets on the Circle

Daniel Berend
, Yuval Peres
, Yuval Peres

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Given an infinite closed subset A of the circle group T, we consider sequences of integers n_j such that n_jA → T in the Hausdorff metric. We prove the existence of a sequence of squares possessing this property and also a sequence of density 1. Quantitative versions for finite A are established as well.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	Journal of the London Mathematical Society
Volume	s2-47
Issue number	1
DOIs	https://doi.org/10.1112/jlms/s2-47.1.1
State	Published - 1 Jan 1993

ASJC Scopus subject areas

General Mathematics

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title = "Asymptotically Dense Dilations of Sets on the Circle",

abstract = "Given an infinite closed subset A of the circle group T, we consider sequences of integers nj such that njA → T in the Hausdorff metric. We prove the existence of a sequence of squares possessing this property and also a sequence of density 1. Quantitative versions for finite A are established as well.",

author = "Daniel Berend and Yuval Peres and Yuval Peres",

year = "1993",

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doi = "10.1112/jlms/s2-47.1.1",

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AU - Peres, Yuval

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N2 - Given an infinite closed subset A of the circle group T, we consider sequences of integers nj such that njA → T in the Hausdorff metric. We prove the existence of a sequence of squares possessing this property and also a sequence of density 1. Quantitative versions for finite A are established as well.

AB - Given an infinite closed subset A of the circle group T, we consider sequences of integers nj such that njA → T in the Hausdorff metric. We prove the existence of a sequence of squares possessing this property and also a sequence of density 1. Quantitative versions for finite A are established as well.

UR - https://www.scopus.com/pages/publications/84963046782

U2 - 10.1112/jlms/s2-47.1.1

DO - 10.1112/jlms/s2-47.1.1

M3 - Article

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EP - 17

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 1

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Asymptotically Dense Dilations of Sets on the Circle

Abstract

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