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

作者信息

Rogers Tim, Castillo Isaac Pérez

机构信息

Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom.

出版信息

Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jan;79(1 Pt 1):012101. doi: 10.1103/PhysRevE.79.012101. Epub 2009 Jan 21.

DOI:10.1103/PhysRevE.79.012101
PMID:19257087
Abstract

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.

摘要

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