Optimal transport is an interesting and exciting application of measure theory to optimization and analysis. In the following, I will bring you through a detailed treatment of random variable couplings, transport plans, basic properties of transport plans, and finishing with the Wasserstein distance on spaces of probability measures with compact support. No detail is left out in this presentation, but some results have further generality and more intricate consequences when tools like measure disintegration are used. But this is left for future work.
Vandegriffe, Austin G., "A Brief on Optimal Transport" (2020). Graduate Student Research & Creative Works. 3.
Mathematics and Statistics
Keywords and Phrases
Optimal Transport; Wasserstein Distance; Probability Theory; Functional Analysis; Optimization
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