Asymptotic Freeness Almost Everywhere for Random Matrices
نویسندگان
چکیده
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. 1991 Mathematics Subject Classification. Primary 15A52; Secondary 62E20, 60F99.
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