Cavity approach to the spectral density of non-Hermitian sparse matrices

Details Cavity approach to the spectral density of non-Hermitian sparse matrices Cavity approach to the spectral density of non-Hermitian sparse matrices

2008-10-06

arxiv.org/abs/0810.0991v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 figures

Scientific paper

10.1103/PhysRevE.79.012101

The spectral densities of ensembles of non-Hermitian sparse random matrices are analysed using the cavity method. We present a set of equations from which the spectral density of a given ensemble can be efficiently and exactly calculated. Within this approach, the generalised Girko's law is recovered easily. We compare our results with direct diagonalisation for a number of random matrix ensembles, finding excellent agreement.

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