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

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.

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.