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

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

2003-01-09

arxiv.org/abs/cond-mat/0301127v1

Phys. Rev. E 67, 047101 (2003)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 5 figures

Scientific paper

10.1103/PhysRevE.67.047101

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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