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• W2076942619 abstract "We analyze the numerical range of high-dimensional random matrices, obtaining limit results and corresponding quantitative estimates in the non-limit case. For a large class of random matrices their numerical range is shown to converge to a disc. In particular, numerical range of complex Ginibre matrix almost surely converges to the disk of radius $sqrt{2}$. Since the spectrum of non-hermitian random matrices from the Ginibre ensemble lives asymptotically in a neighborhood of the unit disk, it follows that the outer belt of width $sqrt{2}-1$ containing no eigenvalues can be seen as a quantification the non-normality of the complex Ginibre random matrix. We also show that the numerical range of upper triangular Gaussian matrices converges to the same disk of radius $sqrt{2}$, while all eigenvalues are equal to zero and we prove that the operator norm of such matrices converges to $sqrt{2e}$." @default.
• W2076942619 created "2016-06-24" @default.
• W2076942619 creator A5035083217 @default.
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• W2076942619 date "2014-10-01" @default.
• W2076942619 modified "2023-09-25" @default.
• W2076942619 title "Numerical range for random matrices" @default.
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• W2076942619 doi "https://doi.org/10.1016/j.jmaa.2014.03.072" @default.
• W2076942619 hasPublicationYear "2014" @default.
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