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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The work of this author was partially supported by NSF Grant DMS-0804133 and by a Grant from the Israel Science Foundation. This work was partially supported by the ANR Project ANR-08-BLAN-0311-01. Attribute ANR support to A. Guionnet, NSF and Israel Science foundation to O. Zeitouni.
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Guionnet, A., Zeitouni, O. Support convergence in the single ring theorem. Probab. Theory Relat. Fields 154, 661–675 (2012). https://doi.org/10.1007/s00440-011-0380-5
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DOI: https://doi.org/10.1007/s00440-011-0380-5
Keywords
- Random matrices
- Non-commutative measure
- Schwinger–Dyson equation
Mathematics Subject Classification (2010)
- 15A52 (46L50, 46L54)