0 A ug 2 00 3 Non - commutative Polynomials of Independent Gaussian Random Matrices . The Real and Symplectic Cases
نویسنده
چکیده
In [HT2] Haagerup and Thorbjørnsen prove the following extension of Voiculescu’s random matrix model (cf. [V2, Theorem 2.2]): For each n ∈ N, let X 1 , . . . ,X (n) r be a system of r independent complex self-adjoint random matrices from the class SGRM(n, 1 n), and let x1, . . . , xr be a semicircular system in a C ∗-probability space. Then for any polynomial p in r non-commuting variables the convergence lim n→∞ ‖p(X 1 , . . . ,X r )‖ = ‖p(x1, . . . , xr)‖ holds almost surely. We generalize this result to sets of independent Gaussian random matrices with real or symplectic entries (the GOEand the GSE-ensembles) and random matrix ensembles related to these.
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