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Consider the Monge-Kantorovich problem of transporting densities $\rho_0$ to $\rho_1$ on $\mathbb{R}^d$ with a strictly convex cost function.
The geometry of optimal transportation
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Gradient flows: In Metric Spaces and in the Space of Probability Measures, 2nd. Edition
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A second order equation for Schrödinger bridges with applications to the hot gas experiment and entropic transportation cost
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From large deviations to Wasserstein gradient flows in multiple dimensions
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