Euclidean quotients of finite metric spaces

Manor Mendel; Assaf Naor

doi:10.1016/j.aim.2003.12.001

Euclidean quotients of finite metric spaces

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

Abstract

This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M and α≥1, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain asymptotically tight bounds for these questions, and prove that they exhibit phase transitions. We also study the analogous problem for embeddings into ℓ_p, and the particular case of the hypercube.

Original language	English
Pages (from-to)	451-494
Number of pages	44
Journal	Advances in Mathematics
Volume	189
Issue number	2
DOIs	https://doi.org/10.1016/j.aim.2003.12.001
State	Published - 20 Dec 2004
Externally published	Yes

Bibliographical note

Funding Information:
·Corresponding author. Fax: +1-425-936-7329. E-mail addresses: [email protected] (M. Mendel), [email protected] (A. Naor). 1Supported in part by a grant from the Israeli Science Foundation (195/02), and by the Landau Center.

Access to Document

10.1016/j.aim.2003.12.001

Cite this

@article{e965891d808642eeb57762d583c7f6c6,

title = "Euclidean quotients of finite metric spaces",

abstract = "This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M and α≥1, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain asymptotically tight bounds for these questions, and prove that they exhibit phase transitions. We also study the analogous problem for embeddings into ℓp, and the particular case of the hypercube.",

author = "Manor Mendel and Assaf Naor",

year = "2004",

month = dec,

day = "20",

doi = "10.1016/j.aim.2003.12.001",

language = "אנגלית",

volume = "189",

pages = "451--494",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Euclidean quotients of finite metric spaces

AU - Mendel, Manor

AU - Naor, Assaf

PY - 2004/12/20

Y1 - 2004/12/20

N2 - This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M and α≥1, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain asymptotically tight bounds for these questions, and prove that they exhibit phase transitions. We also study the analogous problem for embeddings into ℓp, and the particular case of the hypercube.

AB - This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M and α≥1, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain asymptotically tight bounds for these questions, and prove that they exhibit phase transitions. We also study the analogous problem for embeddings into ℓp, and the particular case of the hypercube.

UR - http://www.scopus.com/inward/record.url?scp=4344706090&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2003.12.001

DO - 10.1016/j.aim.2003.12.001

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:4344706090

SN - 0001-8708

VL - 189

SP - 451

EP - 494

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 2

ER -

Euclidean quotients of finite metric spaces

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this