TY - JOUR
T1 - Spectrum of large random asymmetric matrices
AU - Sommers, H. J.
AU - Crisanti, A.
AU - Sompolinsky, H.
AU - Stein, Y.
PY - 1988
Y1 - 1988
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/0000435159
U2 - 10.1103/PhysRevLett.60.1895
DO - 10.1103/PhysRevLett.60.1895
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AN - SCOPUS:0000435159
SN - 0031-9007
VL - 60
SP - 1895
EP - 1898
JO - Physical Review Letters
JF - Physical Review Letters
IS - 19
ER -