B. Khoruzhenko, LARGE-N EIGENVALUE DISTRIBUTION OF RANDOMLY PERTURBED ASYMMETRIC MATRICES, Journal of physics. A, mathematical and general, 29(7), 1996, pp. 165-169
The density of complex eigenvalues of random asymmetric N x N matrices
is found in the large-N limit. The matrices are of the form H-0 + A w
here A is a matrix of N-2 independent, identically distributed random
variables with zero mean and variance N(-1)upsilon(2). The limiting de
nsity rho(z, z) is bounded. The area of the support of rho(z, z*) can
not be less than pi upsilon(2). In the case of H-0 commuting with its
conjugate, rho(z, z) is expressed in terms of the eigenvalue distribu
tion of the non-perturbed part H-0.