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

Department of Computer Science

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

14 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

Access to Document

10.1112/jlms/s2-47.1.1

Cite this

@article{f6b97ffd589e4efa884bed3649871fc8,

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",

month = jan,

day = "1",

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

language = "English",

volume = "s2-47",

pages = "1--17",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "John Wiley and Sons Ltd",

number = "1",

}

TY - JOUR

T1 - Asymptotically Dense Dilations of Sets on the Circle

AU - Berend, Daniel

AU - Peres, Yuval

PY - 1993/1/1

Y1 - 1993/1/1

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 - http://www.scopus.com/inward/record.url?scp=84963046782&partnerID=8YFLogxK

U2 - 10.1112/jlms/s2-47.1.1

DO - 10.1112/jlms/s2-47.1.1

M3 - Article

AN - SCOPUS:84963046782

SN - 0024-6107

VL - s2-47

SP - 1

EP - 17

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 1

ER -

Asymptotically Dense Dilations of Sets on the Circle

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this