Euclidean quotients of finite metric spaces

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticlepeer-review


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
Pages (from-to)451-494
Number of pages44
JournalAdvances in Mathematics
Issue number2
StatePublished - 20 Dec 2004
Externally publishedYes

Bibliographical note

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


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