Stein kernels and moment maps
Probability
2023-06-08 v3 Analysis of PDEs
Functional Analysis
Statistics Theory
Statistics Theory
Abstract
We describe a construction of Stein kernels using moment maps, which are solutions to a variant of the Monge-Amp\`ere equation. As a consequence, we show how regularity bounds 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.
Cite
@article{arxiv.1804.04699,
title = {Stein kernels and moment maps},
author = {Max Fathi},
journal= {arXiv preprint arXiv:1804.04699},
year = {2023}
}
Comments
v2: improved dependence on the dimension in the quantitative CLT. v3: corrected a wrong sentence, which does not affect the results or the proofs