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

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

2008-09-16

arxiv.org/abs/0809.2726v2

J. Phys. A. Vol 41, 502001 (2008) (Fast Track Communications)

Physics

Mathematical Physics

10 pages, 1 figure

Scientific paper

10.1088/1751-8113/41/50/502001

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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