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6. Transportation Cost and Wasserstein Spaces


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      Problem 6.1.

      [Mikhail Ostrovskii] Does there exist a function $f: [0,\infty) \to [0,\infty)$ such that, for every finite metric space $M$, the distortion of $M$ into convex combinations of dominating tree metrics is bounded by $f(c_1(W_1(M)))$?


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          Problem 6.2.

          [Erik Waingarten] Let $M$ be a metric space and $Y$ the subset of $W_1(M)$ consisting of uniform distributions over $s$-point subsets of $M$. Can $c_1(Y)$ be bounded by a function of $s$?


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              Problem 6.3.

              [Mikhail Ostrovskii] Let $\{G_n\}_{n=1}^\infty$ be a sequence of bounded degree expanders. Does the $\ell_2$-sum $(\oplus_n \mathrm{TC}(G_n))_2$ have trivial cotype?

                  Cite this as: AimPL: Metric embeddings, available at http://aimpl.org/metricembeddings.