Explicit expressions are proven for higher-order and mixed derivatives of determinant and Pfaffian ratios over Vandermonde determinants in random matrix theory.
Ratios of characteristic polynomials in complex matrix models
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abstract
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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Derivative relations for determinants, Pfaffians and characteristic polynomials in random matrix theory
Explicit expressions are proven for higher-order and mixed derivatives of determinant and Pfaffian ratios over Vandermonde determinants in random matrix theory.