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arXiv:2010.04291 [math.PR]AbstractReferencesReviewsResources

A Brief on Optimal Transport

Austin Vandegriffe

Published 2020-10-08Version 1

The presentation covers prerequisite results from Topology and Measure Theory. This is then followed by an introduction into couplings and basic definitions for optimal transport. The Kantrorovich problem is then introduced and an existence theorem is presented. Following the setup of optimal transport is a brief overview of the Wasserstein distance and a short proof of how it metrizes the space of probability measures on a COMPACT domain. This presentation is a detailed examination of Villani's "Optimal Transport: Old and New" chapters 1-4 and part of 6.

Comments: This is the script for a brief lecture I gave on optimal transport during the Spring of 2020
Categories: math.PR
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