# Existence and consistency of Wasserstein barycenters

@article{LeGouic2015ExistenceAC, title={Existence and consistency of Wasserstein barycenters}, author={Thibaut Le Gouic and Jean-Michel Loubes}, journal={Probability Theory and Related Fields}, year={2015}, volume={168}, pages={901-917} }

Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random probabilities defined on a geodesic space (E, d). We also prove the consistency of this barycenter in a general setting, that includes taking barycenters of empirical versions of the probability measures or of a growing set of probability measures.

## 100 Citations

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