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The optimal matching problem

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The optimal matching problem is about the rate of convergence in Wasserstein distance of the empirical measure of iid uniform points to the Lebesgue measure. We will start by reviewing the macroscopic behaviour of the matching problem and will then report on recent results on the mesoscopic behaviour in the thermodynamic regime. These results rely on a quantitative large-scale linearization of the Monge-Ampere equation through the Poisson equation. This is based on joint work with Michael Goldman and Felix Otto.

This talk is part of the Probability series.

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