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arxiv: 1009.3856 · v1 · pith:FMT5JHT5new · submitted 2010-09-20 · 🧮 math.CA · math.AP· math.DG· math.PR

Introduction to Optimal Transport Theory

Filippo Santambrogio (CEREMADE) This is my paper
classification 🧮 math.CA math.APmath.DGmath.PR
keywords optimaltransporttheoryconstituteconvexcoursecrashdetailed
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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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  1. Multiscaling in Wasserstein Spaces

    math.NA 2025-09 unverdicted novelty 7.0

    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.