Spectrum of large random asymmetric matrices

The average eigenvalue distribution of N×N real random asymmetric matrices Jij (Jji Jij) is calculated in the limit of Nz. It is found that () is uniform in an ellipse, in the complex plane, whose real and imaginary axes are 1+ and 1-, respectively. The parameter is given by =N[JijJji]J and N[Jij2]J is normalized to 1. In the =1 limit, Wigner's semicircle law is recovered. The results are extended to complex asymmetric matrices.