Stein kernels and moment maps

By Max Fathi. Annals of Probability, 2018

49 citations recorded by the source corpus.

We describe a construction of Stein kernels using moment maps, which are solutions to a variant of the Monge-Ampere 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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e764bbd5785c84e8014e9162192a821a22877c9a

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Improved central limit theorem and bootstrap approximations in high dimensions (2019, background): “The latter result is based on the fact that random vectors with log-concave densities admit Stein kernels with sub-Weibull entries, which is established by Fathi in [24].”
High-dimensional central limit theorems by Stein’s method (2020, methodology): “We prove our main results using the approach of Götze (1991) in Stein’s method, together with modifications of an estimate of Anderson, Hall and Titterington (1998) and a smoothing inequality of Bhattacharya and Rao (1976).”