Contributions to the Theory of Statistical Optimal Transport

Abstract

The goals of this chapter are twofold. First, to provide a summary representation of the core findings on optimal transport that I have worked on in the course of my PhD time. Second, to clarify my own contributions to the research papers A to D, which are the joint product of multiple authors each.The first section contains a brief introduction into the topic of optimal transport with a focus on duality, and serves to prepare the notation and concepts referred to by the rest of the chapter. All of the facts presented here are standard in the theory of optimal transport and can be found in the first chapters of the books by Villani 2008 and Santambrogio 2015. The remaining sections form an attempt to lay out the most important insights stemming from my work in a way that is digestible for non-experts. In doing so, I focus on conceptual points and largely refrain from emphasizing technical aspects, for which the corresponding research papers can be consulted.