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July 2019 Stein kernels and moment maps
Max Fathi
Ann. Probab. 47(4): 2172-2185 (July 2019). DOI: 10.1214/18-AOP1305

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.

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Max Fathi. "Stein kernels and moment maps." Ann. Probab. 47 (4) 2172 - 2185, July 2019. https://doi.org/10.1214/18-AOP1305

Information

Received: 1 June 2018; Revised: 1 August 2018; Published: July 2019
First available in Project Euclid: 4 July 2019

zbMATH: 07114714
MathSciNet: MR3980918
Digital Object Identifier: 10.1214/18-AOP1305

Subjects:
Primary: 60F05
Secondary: 35J96

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 4 • July 2019
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