Asymptotic Freeness Almost Everywhere for Random Matrices
Fumio Hiai and Denes Petz
Voiculescu's asymptotic freeness result for random matrices is improved
to the sense of almost everywhere convergence. The asymptotic freeness almost
everywhere is first shown for standard unitary matrices based on the computation
of multiple moments of their entries, and then it is shown for rather general unitarily
invariant selfadjoint random matrices (in particular, standard selfadjoint Gaussian matrices)
by applying the first result to the unitary parts of their
diagonalization. Bi-unitarily invariant non-selfadjoint random matrices are
also treated via polar decomposition.
Availability: [ gzipped
[ Help on down-loading/viewing/printing
This paper has now been published in
Acta Sci. Math. (Szeged) 66 (2000), no. 3-4, 809--834.