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Stein kernels and moment maps (1804.04699v3)
Published 12 Apr 2018 in math.PR, math.AP, math.FA, math.ST, and stat.TH
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.