[Banach] Abstract of a paper by James R. Lee, Assaf Naor, and Yuval Peres

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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