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

Reference:

Rogers, T. and Perez Castillo, I., 2009. Cavity approach to the spectral density of non-Hermitian sparse matrices. Physical Review E, 79, 012101.

Related documents:

Official URL:

http://dx.doi.org/10.1103/PhysRevE.79.012101

Related URLs:

• http://arxiv.org/abs/0810.0991

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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