Colloquium| Institute of Mathematical Sciences
Time：14:00-15:00, December 19, Thursday
Location：Room S408, IMS
Speaker: Lei Yu, National University of Singapore
Abstract: In this work, we consider Strassen's version of optimal transport problem. That is, we minimize the excess-cost probability (i.e., the probability that the cost is larger than a given value) over all couplings of two distributions. We derive large deviation, moderate deviation, and central limit theorems for this problem. Our approach is based on Strassen's dual formulation of the optimal transport problem, Sanov's theorem on the large deviation principle (LDP) of empirical measures, as well as the moderate deviation principle (MDP) and central limit theorems (CLT) of empirical measures. Finally, we connect Strassen's optimal transport problem to the empirical optimal transport problem, which hence provides an application for our results.