Yi Wei et al 2009 J. Phys. A: Math. Theor. 42 462002 doi:10.1088/1751-8113/42/46/462002
Yi Wei1, Boris A Khoruzhenko2 and Yan V Fyodorov1
Show affiliationsWe show that the density of complex eigenvalues for unitary invariant ensembles of complex matrices A can be written as an integral over the eigenvalues gj of AA†. For the standard random matrix ensembles with matrix density of the form ∏jw(gj), this integral can be further reduced to a twofold integral involving the Christoffel–Darboux kernel for the orthogonal polynomials associated with weight w.
15A18 Eigenvalues, singular values, and eigenvectors
45E05 Integral equations with kernels of Cauchy type (See also 35J15)
Issue 46 (20 November 2009)
Received 17 August 2009, in final form 23 September 2009
Published 22 October 2009
Yi Wei et al 2009 J. Phys. A: Math. Theor. 42 462002
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