Distribution of Eigenvalues of Ensembles of Asymmetrically Diluted Hopfield Matrices

Abstract

Using Grassmann variables and an analogy with two dimensional electrostatics, we obtain the average eigenvalue distribution $\rho (\omega )$ of ensembles of $N\times N$ asymmetrically diluted Hopfield matrices in the limit $N\to \infty$. We found that in the limit of strong dilution the distribution is uniform in a circle in the complex plane.

arXiv comment9 pages, latex, 4 figures

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