Moments of the characteristic polynomial in the three ensembles of random matrices

M. L. Mehta; J. -M. Normand

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Moments of the characteristic polynomial in the three ensembles of random matrices

M. L. Mehta·J. -M. Normand

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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 comparing the two expressions of the same moment one gets two remarkable identities, one between an $n\times n$ determinant and an $m\times m$ determinant and another between the pfaffian of a $2n\times 2n$ anti-symmetric matrix and a sum of $m\times m$ determinants.

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M. L. Mehta, J. -M. Normand. 2001-05-23. Moments of the characteristic polynomial in the three ensembles of random matrices. https://arxiv.org/abs/cond-mat/0101469

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