Abstract
We study in the limit of infinite matrix order the normalized eigenvalue counting measures of the commutator and anticommutator of two Hermitian (or real symmetric) matrices rotated independently one respect to another by the random unitary (or orthogonal) Haar distributed matrix. We establish the convergence with probability 1 to a limiting nonrandom measure. We obtain and analyze the functional equations for the Stieltjes transforms of the limiting measures.
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