Abstract
We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if and only if it does not contain arbitrarily large complete binary trees with uniformly bounded distortion. We also introduce a new metric invariant called Markov convexity, and show how it can be used to compute the Euclidean distortion of any metric tree up to universal factors.
Original language | English (US) |
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Pages (from-to) | 1609-1659 |
Number of pages | 51 |
Journal | Geometric and Functional Analysis |
Volume | 18 |
Issue number | 5 |
DOIs | |
State | Published - Feb 2009 |
Keywords
- Metric trees
- Uniform convexity
- bi-Lipschitz embeddings
ASJC Scopus subject areas
- Analysis
- Geometry and Topology