Moments of the characteristic polynomial in the three ensembles of random matrices
Résumé
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.
Domaines
Physique mathématique [math-ph]
Origine : Fichiers produits par l'(les) auteur(s)
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