Stein kernels and moment maps

Max Fathi

doi:10.1214/18-aop1305

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arXiv · 1804.04699

Stein kernels and moment maps

Max Fathi

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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.

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Max Fathi. 2018-04-12. Stein kernels and moment maps. https://doi.org/10.1214/18-aop1305

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