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. © 1988 The American Physical Society.
SPECTRUM OF LARGE RANDOM ASYMMETRIC MATRICES / H. J., Sommers; Crisanti, Andrea; H., Sompolinsky; Y., Stein. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - STAMPA. - 60:19(1988), pp. 1895-1898. [10.1103/physrevlett.60.1895]
SPECTRUM OF LARGE RANDOM ASYMMETRIC MATRICES
CRISANTI, Andrea;
1988
Abstract
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. © 1988 The American Physical Society.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
