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

Yan V Fyodorov·Boris A Khoruzhenko
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Abstract

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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Yan V Fyodorov, Boris A Khoruzhenko. 2006-08-03. On absolute moments of characteristic polynomials of a certain class of complex random matrices. https://doi.org/10.1007/s00220-007-0270-y

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