Recognition: unknown
Derivative moments for characteristic polynomials from the CUE
classification
🧮 math.PR
keywords
matrixmomentscharacteristicderivativerandomsizeunitaryallows
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We calculate joint moments of the characteristic polynomial of a random unitary matrix from the circular unitary ensemble and its derivative in the case that the power in the moments is an odd positive integer. The calculations are carried out for finite matrix size and in the limit as the size of the matrices goes to infinity. The latter asymptotic calculation allows us to prove a long-standing conjecture from random matrix theory.
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Cited by 1 Pith paper
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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.
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