title: Localization transition in symmetric random matrices.
abstract: We study the behavior of the inverse participation ratio and the localization transition in infinitely large random matrices through the cavity method. Results are shown for two ensembles of random matrices: Laplacian matrices on sparse random graphs and fully connected Lévy matrices. We derive a critical line separating localized from extended states in the case of Lévy matrices. Comparison between theoretical results and diagonalization of finite random matrices is shown.
authors.affiliation: Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium.
authors.forename: F L
authors.initials: FL
authors.lastname: Metz
authors.forename: I
authors.initials: I
authors.lastname: Neri
authors.forename: D
authors.initials: D
authors.lastname: Bollé