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Mathematics  2014 

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

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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 $({\mathcal A},\varphi)$ 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.

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