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arXiv · 0706.0545

Trees and Markov convexity

James R. Lee·Assaf Naor·Yuval Peres
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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.

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James R. Lee, Assaf Naor, Yuval Peres. 2007-06-04. Trees and Markov convexity. https://arxiv.org/abs/0706.0545

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