We review a new technique for calculating spectral properties of infinite non-Hermitian random matrix models, and we present an algorithm for calculating bulk spectral properties of ensembles of the type H1 + i H2, where H1 and H2 are arbitrary free (in the sense of Voiculescu) ensembles, including cases of the Lévy (heavy-tailed) spectra. As a particular example, we solve analytically the ensemble C1 + i C2, where C1 and C2 are free centered random matrix ensembles of the Cauchy class.
PACS numbers: 02.10.Yn, 02.50.Cw, 05.40.Fb
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