This is an announcement for the paper "Trees and Markov convexity" by James R. Lee, Assaf Naor, and Yuval Peres.

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.

Archive classification: math.MG math.FA

The source file(s), TreeMarkov-GAFA.tex: 228845 bytes

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http://arXiv.org/abs/0706.0545

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