title: Equivalence of replica and cavity methods for computing spectra of sparse random matrices.
abstract: We show by direct calculation that the replica and cavity methods are exactly equivalent for the spectrum of an Erdős-Rényi random graph. We introduce a variational formulation based on the cavity method and use it to find approximate solutions for the density of eigenvalues. We also use this variational method for calculating spectra of sparse covariance matrices.
authors.affiliation: Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic. slanina@fzu.cz
authors.forename: František
authors.initials: F
authors.lastname: Slanina