TY - JOUR

T1 - Euclidean quotients of finite metric spaces

AU - Mendel, Manor

AU - Naor, Assaf

N1 - 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.

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

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U2 - 10.1016/j.aim.2003.12.001

DO - 10.1016/j.aim.2003.12.001

M3 - Article

AN - SCOPUS:4344706090

SN - 0001-8708

VL - 189

SP - 451

EP - 494

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 2

ER -