Euclidean quotients of finite metric spaces

Details Euclidean quotients of finite metric spaces Euclidean quotients of finite metric spaces

2004-06-17

arxiv.org/abs/math/0406349v1

Adv. Math. 189(2) 451-494, 2004

Mathematics

Metric Geometry

36 pages, 0 figures. To appear in Advances in Mathematics

Scientific paper

10.1016/j.aim.2003.12.001

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, 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 embedings into l_p, and the particular case of the hypercube.

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