Year: 2019
Type: article
Abstract: We describe a construction of Stein kernels using moment maps, which are solutions to a variant of the Monge–Ampère equation. As a consequence, we show how regularity bounds in certain weighted Sobolev spaces on these maps control the rate of convergence in the classical central limit theorem, and derive new rates in Kantorovitch–Wasserstein distance in the log-concave situation, with explicit polynomial dependence on the dimension.
Source: The Annals of Probability
DOI: 10.1214/18-aop1305
Author: Max Fathi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2797598944