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On random symmetric matrices with a constraint: the spectral density of random impedance networks

J. Staering·B. Mehlig·Yan V. Fyodorov·J. M. Luck
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Abstract

We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found recently for the average density of resonances in random impedance networks [Y.V. Fyodorov, J. Phys. A: Math. Gen. 32, 7429 (1999)]. In the case of banded matrices, the analytical results are compared with those extracted from the numerical solution of Kirchhoff equations for quasi one-dimensional random impedance networks.

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J. Staering, B. Mehlig, Yan V. Fyodorov, J. M. Luck. 2003-01-09. On random symmetric matrices with a constraint: the spectral density of random impedance networks. https://doi.org/10.1103/physreve.67.047101

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