Averages of Spectral Determinants and `Single Ring Theorem' of Feinberg and Zee

We compute < det (Iz-H) (Iz-H)^dagger rangle _H in the limit of infinite matrix dimension N for complex random matrices H with invariant matrix distribution in terms of the eigenvalue distribution of the Hermitian random matrices HH^dagger . Under the assumption that 1 over N ln < det (Iz-H) (Iz-H)^dagger rangle _H is asymptotically equal to 1over N < ln det (Iz-H) (Iz-H)^dagger rangle _H we reproduce the eigenvalue distribution of H obtained previously by Feinberg and Zee, Nucl. Phys. B501, 643 (1997).