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math.FA2013★ 16 cited
A geometric study of Wasserstein spaces: ultrametrics
Benoît Kloeckner
We study the geometry of the space of measures of a compact ultrametric space X, endowed with the L^p Wasserstein distance from optimal transportation. We show that the power p of…
math.FA2013
Yet another short proof of Bourgain's distorsion estimate
Benoît Kloeckner
We use a self-improvement argument to give a very short and elementary proof of the result of Bourgain saying that regular trees do not admit bi-Lipschitz embeddings into uniformly…