Limiting spectral distribution of sums of unitary and orthogonal matrices∗
نویسندگان
چکیده
We show that the empirical eigenvalue measure for sum of d independent Haar distributed n-dimensional unitary matrices, converge for n → ∞ to the Brown measure of the free sum of d Haar unitary operators. The same applies for independent Haar distributed n-dimensional orthogonal matrices. As a byproduct of our approach, we relax the requirement of uniformly bounded imaginary part of Stieltjes transform of Tn that is made in [7, Thm. 1].
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