Differential equations isolate N-dependent terms in edge density expansions for classical random matrix ensembles, yielding explicit correction terms at the hard edge.
Forrester,Dualities in random matrix theory
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Explicit expressions are proven for higher-order and mixed derivatives of determinant and Pfaffian ratios over Vandermonde determinants in random matrix theory.
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Edge density expansions for the classical Gaussian and Laguerre ensembles
Differential equations isolate N-dependent terms in edge density expansions for classical random matrix ensembles, yielding explicit correction terms at the hard edge.
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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.