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arXiv · 0809.2726

On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values

Yi Wei·Yan V. Fyodorov
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Abstract

Given any fixed $N \times N$ positive semi-definite diagonal matrix $G\ge 0$ we derive the explicit formula for the density of complex eigenvalues for random matrices $A$ of the form $A=U\sqrt{G}$} where the random unitary matrices $U$ are distributed on the group $\mathrm{U(N)}$ according to the Haar measure.

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Yi Wei, Yan V. Fyodorov. 2008-11-10. On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values. https://doi.org/10.1088/1751-8113%2F41%2F50%2F502001

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