Asymptotics of Smoothed Wasserstein Distances

@article{Chen2020AsymptoticsOS,
  title={Asymptotics of Smoothed Wasserstein Distances},
  author={Hong-Bin Chen and Jonathan Niles-Weed},
  journal={arXiv: Probability},
  year={2020}
}
We investigate contraction of the Wasserstein distances on $\mathbb{R}^d$ under Gaussian smoothing. It is well known that the heat semigroup is exponentially contractive with respect to the Wasserstein distances on manifolds of positive curvature; however, on flat Euclidean space---where the heat semigroup corresponds to smoothing the measures by Gaussian convolution---the situation is more subtle. We prove precise asymptotics for the $2$-Wasserstein distance under the action of the Euclidean… 

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