title: Cavity approach to the spectral density of non-Hermitian sparse matrices.
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.
authors.affiliation: Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom.
authors.forename: Tim
authors.initials: T
authors.lastname: Rogers
authors.forename: Isaac Pérez
authors.initials: IP
authors.lastname: Castillo