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

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.

4 pages, 3 figures

References in corpus (2)

• Cavity Approach to the Spectral Density of Sparse Symmetric Random Matrices
• Spectra of Sparse Random Matrices

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