The single ring theorem
نویسندگان
چکیده
Abstract We study the empirical measure LAn of the eigenvalues of non-normal square matrices of the form An = UnTnVn with Un,Vn independent Haar distributed on the unitary group and Tn real diagonal. We show that when the empirical measure of the eigenvalues of Tn converges, and Tn satisfies some technical conditions, LAn converges towards a rotationally invariant measure μ on the complex plane whose support is a single ring. In particular, we provide a complete proof of Feinberg-Zee single ring theorem [6]. We also consider the case where Un,Vn are independent Haar distributed on the orthogonal group.
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