Sharp comparison between the 1-Wasserstein distance and its sliced version

Mathphys Analysis Seminar

Wasserstein distances are known to be costly to compute in high dimensions, this is why their sliced variants that only involve their one-dimensional projections have been proposed as a tractable surrogate, indeed quite popular in applications. But how reliable is really this surrogate? In this talk, based on a joint work with Alessio Figalli, Quentin Mrigot and Yi Wang, I will discuss some sharp comparison results.