On absolute moments of characteristic polynomials of a certain class of complex random matrices

Details On absolute moments of characteristic polynomials of a certain class of complex random matrices On absolute moments of characteristic polynomials of a certain class of complex random matrices

2006-02-13

arxiv.org/abs/math-ph/0602032v2

Commun. Math. Phys. 273, 561-599 (2007)

Physics

Mathematical Physics

41 page, typos corrected

Scientific paper

10.1007/s00220-007-0270-y

Integer moments of the spectral determinant $|\det(zI-W)|^2$ of complex random matrices $W$ are obtained in terms of the characteristic polynomial of the Hermitian matrix $WW^*$ for the class of matrices $W=AU$ where $A$ is a given matrix and $U$ is random unitary. This work is motivated by studies of complex eigenvalues of random matrices and potential applications of the obtained results in this context are discussed.

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