A multiscale framework for probability measures in Wasserstein spaces is developed, including a refinement operator preserving geodesic structure and an optimality number for detecting non-geodesic dynamics across scales.
Introduction to Optimal Transport Theory
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abstract
These notes constitute a sort of Crash Course in Optimal Transport Theory. The different features of the problem of Monge-Kantorovitch are treated, starting from convex duality issues. The main properties of space of probability measures endowed with the distances $W_p$ induced by optimal transport are detailed. The key tools to put in relation optimal transport and PDEs are provided.
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2025 1verdicts
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Multiscaling in Wasserstein Spaces
A multiscale framework for probability measures in Wasserstein spaces is developed, including a refinement operator preserving geodesic structure and an optimality number for detecting non-geodesic dynamics across scales.