Optimal transportation with infinitely many marginals
Analysis of PDEs
2012-06-26 v1 Optimization and Control
Abstract
We formulate and study an optimal transportation problem with infinitely many marginals; this is a natural extension of the multi-marginal problem studied by Gangbo and Swiech (1998). We prove results on the existence, uniqueness and characterization of the optimizer, which are natural extensions of the results of Gangbo and Swiech. The proof relies on a relationship between this problem and the problem of finding barycenters in the Wasserstein space, a connection first observed for finitely many marginals by Agueh and Carlier (2011).
Keywords
Cite
@article{arxiv.1206.5515,
title = {Optimal transportation with infinitely many marginals},
author = {Brendan Pass},
journal= {arXiv preprint arXiv:1206.5515},
year = {2012}
}