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.
1988
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/69352
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