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.

翻译：我们证明了矩阵价值值函数的瞬间主要化原则,其域值为$1,1 ⁇ m}$1,1 ⁇ m}$m\in\in\mathb{N}$。该原则是非混合多线性多线性高端时与不同随机矩阵混合输入之间的不平等,每个变量的影响较小,变量是独立即时的。这一技术结果可以被解释为莫塞尔、奥唐奈尔和奥列斯基维茨基茨的原始差异性原则的两种不平等之一的非平衡化概括化。它给出了对非混合噪音稳定性和非混合反浓缩的应用。