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

Abstract

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 X1(n),..., Xr(n) be r independent complex self-adjoint random matrices from the class Open image in new window 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