Distribution of Eigenvalues of Ensembles of Asymmetrically Diluted Hopfield Matrices

Details Distribution of Eigenvalues of Ensembles of Asymmetrically Diluted Hopfield Matrices Distribution of Eigenvalues of Ensembles of Asymmetrically Diluted Hopfield Matrices

1995-01-17

arxiv.org/abs/cond-mat/9501070v1

Physics

Condensed Matter

9 pages, latex, 4 figures

Scientific paper

10.1088/0305-4470/29/15/035

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 $N \rightarrow
\infty$. We found that in the limit of strong dilution the distribution is
uniform in a circle in the complex plane.

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