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math.MG2007
Almost Euclidean subspaces of \ell_1^N via expander codes
Venkatesan Guruswami, James R. Lee, Alexander Razborov
We give an explicit (in particular, deterministic polynomial time) construction of subspaces X of R^N of dimension (1-o(1))N such that for every element x in X, |x|_1 and N^{1/2} |…
math.MG2007
Trees and Markov convexity
James R. Lee, Assaf Naor, Yuval Peres
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…