Moments of the characteristic polynomial in the three ensembles of random matrices
- 24 May 2001
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 34 (22) , 4627-4639
- https://doi.org/10.1088/0305-4470/34/22/304
Abstract
Moments of the characteristic polynomial of a random matrix taken from any of the three ensembles, orthogonal, unitary or symplectic, are given either as a determinant or a Pfaffian or as a sum of determinants. For Gaussian ensembles, on comparing two expressions of the same moment one obtains two remarkable identities, one between an n×n determinant and an m×m determinant and another between the Pfaffian of a 2n×2n anti-symmetric matrix and a sum of m×m determinants.Keywords
This publication has 5 references indexed in Scilit:
- Random matrix theory and the derivative of the Riemann zeta functionProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2000
- Random Matrix Theory and ζ(1/2+ it)Communications in Mathematical Physics, 2000
- Random Matrix Theory and L-Functions at s = 1/2Communications in Mathematical Physics, 2000
- Characteristic Polynomials of Random MatricesCommunications in Mathematical Physics, 2000
- A method of integration over matrix variables: IVJournal de Physique I, 1991