Euclidean quotients of finite metric spaces

By Manor Mendel, Assaf Naor. 2004

82 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/32c90ea3ebe2a4356e286d1f1b9cd78447217488

Citations in the corpus

• The non-linear geometry of Banach spaces after Nigel Kalton (2012, unknown): “= Mendel-Naor papers [67] and [69].”