A Moment Majorization principle for random matrix ensembles

Abstract

We prove a moment majorization principle for matrix-valued functions with domain $\{-1,1{\}}^m$, $m\in \mathbb{N}$. The principle is an inequality between higher-order moments of a non-commutative multilinear polynomial with different random matrix ensemble inputs, where each variable has small influence and the variables are instantiated independently. This technical result can be interpreted as a noncommutative generalization of one of the two inequalities of the seminal invariance principle of Mossel, O'Donnell and Oleszkiewicz. Applications to noncommutative noise stability and noncommutative anticoncentration are given.

27 pages

References in corpus (2)

• Invariance principles for homogeneous sums: Universality of Gaussian Wiener chaos
• Invariance principles for homogeneous sums of free random variables