We study the spectra and localization properties of Euclidean random matrices defined on a random graph. We introduce a powerful method to find the density of states and the localization threshold in topologically disordered (off-lattice) systems. We solve numerically an equation (exact on the random graph) for the probability distribution function of the diagonal elements of the resolvent matrix, with a population dynamics algorithm (PDA). We show that the localization threshold can be estimated by studying the stability of a population of real resolvents under the PDA. An application is given in the context of the instantaneous normal modes of a liquid.
Anderson localization in Euclidean random matrices / S., Ciliberti; T. S., Grigera; V., Martn Mayor; Parisi, Giorgio. - In: PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS. - ISSN 1098-0121. - 71:15(2005), pp. 153104-1-153104-6. [10.1103/physrevb.71.153104]