Moments of the characteristic polynomial in the three ensembles of random matrices
Mehta, M. L. · Normand, J. -M.
Original · EN
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 comparing the two expressions of the same moment one gets 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.
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