A quantitative fourth moment theorem in free probability theory

Guillaume Cébron (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

A quantitative " fourth moment theorem " for any self-adjoint element in a homogeneous Wigner chaos is provided: 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.

Domaines: Mathématiques [math]; Probabilités [math.PR]; Algèbres d'opérateurs [math.OA]

Guillaume Cébron. A quantitative fourth moment theorem in free probability theory. 2018. ⟨hal-01738681⟩