Ratios of characteristic polynomials in complex matrix models

Details Ratios of characteristic polynomials in complex matrix models Ratios of characteristic polynomials in complex matrix models

2004-04-28

arxiv.org/abs/math-ph/0404068v2

J.Phys.A37:L453-L460,2004

Physics

Mathematical Physics

7 pages, notation clarified in published version

Scientific paper

10.1088/0305-4470/37/37/L01

We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as their Cauchy transforms, generalizing previous expressions for real eigenvalues. We restrict ourselves to ratios of characteristic polynomials over their complex conjugate.

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