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• W2951102939 abstract "We study the empirical measure $L_{A_n}$ of the eigenvalues of non-normal square matrices of the form $A_n=U_nD_nV_n$ with $U_n,V_n$ independent Haar distributed on the unitary group and $D_n$ real diagonal. We show that when the empirical measure of the eigenvalues of $D_n$ converges, and $D_n$ satisfies some technical conditions, $L_{A_n}$ converges towards a rotationally invariant measure on the complex plan whose support is a single ring. In particular, we provide a complete proof of Feinberg-Zee single ring theorem cite{FZ}. We also consider the case where $U_n,V_n$ are independent Haar distributed on the orthogonal group." @default.
• W2951102939 created "2019-06-27" @default.
• W2951102939 creator A5000594503 @default.
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• W2951102939 date "2009-09-11" @default.
• W2951102939 modified "2023-09-27" @default.
• W2951102939 title "The single ring theorem" @default.
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• W2951102939 hasPublicationYear "2009" @default.
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