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We develop a theory which describes the behavior of eigenvalues of a class of one-dimensional random non-Hermitian operators introduced recently by Hatano and Nelson. We prove that the eigenvalues are distributed along a curve in the complex plane. An equation for the curve is derived, and the density of complex eigenvalues is found in terms of spectral characteristics of a ``reference'' Hermitian disordered system. The generic properties of the eigenvalue distribution are discussed.
Goldsheid et al. (Mon,) studied this question.