Stein kernels are a way to compare a given probability measure to some reference measure, typically the standard gaussian distribution, via integration by parts formulas. In this talk, I will present a construction of such kernels via optimal transport, and some applications. As a byproduct, we obtain new quantitative bounds on the rate of convergence in the central limit theorem for multidimensional log-concave distributions via regularity theory for Monge-Ampére PDEs.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/7138