Euclidean quotients of finite metric spaces

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)451-494
Number of pages44
JournalAdvances in Mathematics
Volume189
Issue number2
DOIs
StatePublished - Dec 20 2004

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Metric space
Euclidean
Quotient
Hypercube
Phase Transition
Hilbert space
Subset

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Euclidean quotients of finite metric spaces. / Mendel, Manor; Naor, Assaf.

In: Advances in Mathematics, Vol. 189, No. 2, 20.12.2004, p. 451-494.

Research output: Contribution to journalArticle

Mendel, Manor ; Naor, Assaf. / Euclidean quotients of finite metric spaces. In: Advances in Mathematics. 2004 ; Vol. 189, No. 2. pp. 451-494.
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