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

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

2001-01-31

arxiv.org/abs/cond-mat/0101469v3

Physics

Condensed Matter

Statistical Mechanics

tex, 1 file, 15 pages [SPhT-T01/016], published J. Phys. A: Math. Gen. 34 (2001) 1-13

Scientific paper

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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