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Support convergence in the single ring theorem |
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| Authors: | Alice Guionnet Ofer Zeitouni |
| Affiliation: | 1. UMPA, CNRS UMR 5669, ENS Lyon, 46 all??e d??Italie, 69007, Lyon, France 2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA 3. Faculty of Mathematics, Weizmann Institute, POB26, Rehovot, 76100, Israel |
| Abstract: | We study the eigenvalues of non-normal square matrices of the form A n ?=?U n T n V n with U n , V n independent Haar distributed on the unitary group and T n real diagonal. We show that when the empirical measure of the eigenvalues of T n converges, and T n satisfies some technical conditions, all these eigenvalues lie in a single ring. |
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