Limit Theorems for Entropic Optimal Transport Maps and the Sinkhorn Divergence

Understand

We study limit theorems for entropic optimal transport (EOT) maps, dual potentials, and the Sinkhorn divergence.

• The key technical tool we use is a first and second-order Hadamard differentiability analysis of EOT potentials with respect to the marginal distributions, which may be of independent interest.
• Given the differentiability results, the functional delta method is used to obtain central limit theorems for empirical EOT potentials and maps.
• The second-order functional delta method is leveraged to establish the limit distribution of the empirical Sinkhorn divergence under the null.