Explicit expressions are proven for higher-order and mixed derivatives of determinant and Pfaffian ratios over Vandermonde determinants in random matrix theory.
Eigenvalue correlations in non-Hermitean symplectic random matrices
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Correlation function of complex eigenvalues of N by N random matrices drawn from non-Hermitean random matrix ensemble of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are studied in detail in the regimes of weak and strong non-Hermiticity.
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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.