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arXiv · 0810.0991

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

Tim Rogers·Isaac Perez Castillo
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Abstract

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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Tim Rogers, Isaac Perez Castillo. 2008-10-09. Cavity approach to the spectral density of non-Hermitian sparse matrices. https://doi.org/10.1103/physreve.79.012101

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