Products and ratios of characteristic polynomials of random Hermitian matrices
- 1 August 2003
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 44 (8) , 3657-3670
- https://doi.org/10.1063/1.1587875
Abstract
We present new and streamlined proofs of various formulas for products and ratios of characteristic polynomials of random Hermitian matrices that have appeared recently in the literature.Keywords
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This publication has 13 references indexed in Scilit:
- An exact formula for general spectral correlation function of random Hermitian matricesJournal of Physics A: General Physics, 2003
- On the Characteristic Polynomial¶ of a Random Unitary MatrixCommunications in Mathematical Physics, 2001
- Application of the τ-Function Theory¶of Painlevé Equations to Random Matrices:¶PIV, PII and the GUECommunications in Mathematical Physics, 2001
- Random matrix theory and the derivative of the Riemann zeta functionProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2000
- Characteristic Polynomials of Random MatricesCommunications in Mathematical Physics, 2000
- Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theoryCommunications on Pure and Applied Mathematics, 1999
- Strong asymptotics of orthogonal polynomials with respect to exponential weightsCommunications on Pure and Applied Mathematics, 1999
- Correlators of Spectral Determinants in Quantum ChaosPhysical Review Letters, 1995
- A Steepest Descent Method for Oscillatory Riemann--Hilbert Problems. Asymptotics for the MKdV EquationAnnals of Mathematics, 1993
- Discrete Painlevé equations and their appearance in quantum gravityCommunications in Mathematical Physics, 1991