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In [HT2] Haagerup and Thorbjo rnsen prove the following extension of Voiculescu’s random matrix model (cf. [V2, Theorem 2.2]): For each n ∈ ℕ, let X 1 (n),..., X r (n) be r independent complex self-adjoint random matrices from the class and let x 1,..., x r be a semicircular system in a C*-probability space. Then for any polynomial p in r non-commuting variables the convergence holds almost surely. We generalize this result to sets of independent Gaussian random matrices with real or symplectic entries (the GOE- and the GSE-ensembles) and random matrix ensembles related to these.

Non-commutative polynomials of independent Gaussian random matrices. The real and symplectic cases.