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Author ORCID Identifier


Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program


Year Degree Awarded


Month Degree Awarded


First Advisor

Nestor Guillen

Subject Categories



In this work we study a modification of the Monge-Kantorovich problem taking into account path dependence and interaction effects between particles. We prove existence of solutions under mild conditions on the data, and after imposing stronger conditions, we characterize the minimizers by relating them to an auxiliary Monge-Kantorovich problem of the more standard kind. With this notion of how particles interact and travel along paths, we produce a dual problem. The main novelty here is to incorporate an interaction effect to the optimal path transport problem. This covers for instance, N-body dynamics when the underlying measures are discrete. Lastly, our results include an extension of Brenier's theorem on optimal transport maps.


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Creative Commons Attribution-Share Alike 4.0 License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 License.

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