LARGE-N EIGENVALUE DISTRIBUTION OF RANDOMLY PERTURBED ASYMMETRIC MATRICES

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.