The eigenvalue spectrum of a large real antisymmetric random matrix with non-zero mean

Abstract

We study the eigenvalue spectrum of a large real antisymmetric random matrix $J_{ij}$. Using a fermionic approach and replica trick, we obtain a semicircular spectrum of eigenvalues when the mean value of each matrix element is zero, and in the case of a non-zero mean, we show that there is a set of critical finite mean values above which eigenvalues arise that are split off from the semicircular continuum of eigenvalues. The result converged with numerical simulations.

arXiv comment12 pages, added references; 3 figures

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