A quantitative fourth moment theorem in free probability theory

Published 26 Mar 2018 in math.PR and math.OA | (1803.09669v2)

Abstract: A quantitative "fourth moment theorem" is provided for any self-adjoint element in a homogeneous Wigner chaos: the Wasserstein distance is controlled by the distance from the fourth moment to two. The proof uses the free counterpart of the Stein discrepancy. On the way, the free analogue of the WSH inequality is established.

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Guillaume Cébron

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