On the law of multiplication of unitary random matrices

V. Vasilchuk

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov

Abstract: Normalized eigenvalue counting measure of the product of two unitary matrices rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix is studied in the limit of infinite matrix order. Convergence with probability 1 to a limiting nonrandom measure is established. The functional equation for the Herglotz transform of the limiting measure is obtained.

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