Trees and Markov convexity
Metric Geometry
2007-06-06 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.0706.0545,
title = {Trees and Markov convexity},
author = {James R. Lee and Assaf Naor and Yuval Peres},
journal= {arXiv preprint arXiv:0706.0545},
year = {2007}
}