Abstract: One of the central objects in the theory of optimal transport is the Brenier map: the unique monotone transformation which pushes forward an absolutely continuous probability law onto any other given law. Recent work has identified a class of plugin estimators of Brenier maps which achieve the minimax L^2 risk, and are simple to compute. In this talk, we show that such estimators obey pointwise central limit theorems. This provides a first step toward the question of performing statistical…