DISTRIBUTION OF EIGENVALUES IN NON-HERMITIAN ANDERSON MODELS

We develop a theory which describes the behavior of eigenvalues of a c lass of one-dimensional random non-Hermitian operators introduced rece ntly by Hatano and Nelson. We prove that the eigenvalues are distribut ed along a curve in the complex plane. An equation for the curve is de rived, and the density of complex eigenvalues is found in terms of spe ctral characteristics of a ''reference'' Hermitian disordered system. The generic properties of the eigenvalue distribution are discussed.