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

The spectral densities of ensembles of non-Hermitian sparse random matrices are analyzed 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 generalized Girko's law is rec...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2009-01, Vol.79 (1 Pt 1), p.012101-012101, Article 012101
Main Authors: Rogers, Tim, Castillo, Isaac Pérez
Format: Article
Language:English
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Summary:The spectral densities of ensembles of non-Hermitian sparse random matrices are analyzed 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 generalized Girko's law is recovered easily. We compare our results with direct diagonalisation for a number of random matrix ensembles, finding excellent agreement.
ISSN:1539-3755
1550-2376
DOI:10.1103/physreve.79.012101