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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1999-26
August 1999

Mixed Moments of Voiculescu's Gaussian Random Matrices


Steen Thorbjørnsen


It is showed that the convergence of mixed moments of independent, self adjoint, Gaussian random matrices, proved by Voiculescu, holds almost surely, and not only in the mean. This is used to obtain asymptotic lower (respectively upper) bounds on the maximum (respectively minimum) of the spectrum of S*S, for Gaussian random matrices S with operator entries; in particular those studied in [HT2]. Finally a new proof is presented of the result by S. Wassermann, that free group factors can be embedded into ultra products of matrix algebras.

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This paper has now been published in J. Funct. Anal. 176 (2000), no. 2, 213--246.