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

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 $W{W}^{\ast }$ 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.

41 page, typos corrected

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