Random symmetric matrices with a constraint: The spectral density of random impedance networks
Abstract
We derive the mean eigenvalue density for symmetric Gaussian random N×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 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.
- Publication:
-
Physical Review E
- Pub Date:
- April 2003
- DOI:
- 10.1103/PhysRevE.67.047101
- arXiv:
- arXiv:cond-mat/0301127
- Bibcode:
- 2003PhRvE..67d7101S
- Keywords:
-
- 02.50.-r;
- Probability theory stochastic processes and statistics;
- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- 4 pages, 5 figures