Optimal transportation with infinitely many marginals

By Brendan Pass. 2012

53 citations recorded by the source corpus.

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).

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/7a20e31ea8c79c407918e8fe72d2641eaee1394f

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In Applied Mathematics

Citations in the corpus

Consistent estimation of a population barycenter in the Wasserstein space (2013, background): “1) has not been considered in [27] for the characterisation of a population barycenter.”
Bayesian Learning with Wasserstein Barycenters (2018, background): “Let us now recall the Wasserstein barycenter, introduced in [1] and further studied in [35, 25, 28], among others.”
Statistical Aspects of Wasserstein Distances (2018, background): “The results extend to the population version (Pass, 2013): the condition is that with positive probability Λ is absolutely continuous (assuming that the Fr´echet functional F is ﬁnite).”
Wasserstein Barycenters over Riemannian manifolds (2014, background): “The remainder of the proof follows an argument in [32].”
Multi-marginal optimal transport: theory and applications (2014, background): “In this case, the dichotomy described in the earlier examples becomes even more pronounced; for Gangbo−Swiech type costs, the solution again concentrates on graphs over the first marginal [64, 67], but for a class of costs including the Coulomb cost (see Sect.”
Characterization of barycenters in the Wasserstein space by averaging optimal transport maps (2012, background): “3 Related results in the literature A similar notion (to the one in this paper) of a population barycenter and its connection to optimal transportation with infinitely many marginals have been studied in [35].”