On Random Operator-Valued Matrices: Operator-Valued Semicircular Mixtures and Central Limit Theorem

Abstract

Motivated by a random matrix theory model from wireless communications, we define random operator-valued matrices as the elements of $L^{\infty -}(\Omega ,\mathcal{F},\mathbb{P})\otimes M_d(\mathcal{A})$ where $(\Omega ,\mathcal{F},\mathbb{P})$ is a classical probability space and $(\mathcal{A},\phi )$ is a non-commutative probability space. A central limit theorem for the mean $M_d(\mathbb{C})$-valued moments of these random operator-valued matrices is derived. Also a numerical algorithm to compute the mean $M_d(\mathbb{C})$-valued Cauchy transform of operator-valued semicircular mixtures is analyzed.

17 pages, 1 figure

References in corpus (1)

• Random Matrix Systems with Block-Based Behavior and Operator-Valued Models