Estimating transport distances via Stein's method

Stein’s method is a set of techniques for bounding distances between probability measures via integration-by-parts formulas. It was introduced by Stein in the 1980s for bouding the rate of convergence in central limit theorems, and has found many applications since then in probability, statistics and beyond. In this talk, I will present classical variants of this method in the context of estimating $L^1$ Wasserstein distances, and discuss some recent developments for $L^1$ Wasserstein distances.