For random matrices X_n = P_n + iQ_n with P_n and Q_n independently Haar-rotated Hermitian two-atom matrices, the empirical spectral distribution converges almost surely to the Brown measure of p + iq whenever the laws converge.
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Convergence of the Laws of Non-Hermitian Sums of Projections
For random matrices X_n = P_n + iQ_n with P_n and Q_n independently Haar-rotated Hermitian two-atom matrices, the empirical spectral distribution converges almost surely to the Brown measure of p + iq whenever the laws converge.