title: Near-optimal configurations in mean-field disordered systems.
abstract: We present a general technique to compute how the energy of a configuration varies as a function of its overlap with the ground state in the case of optimization problems. Our approach is based on a generalization of the cavity method to a system interacting with its ground state. With this technique we study the random matching problem as well as the mean-field diluted spin glass. As a by-product of this approach we calculate the de Almeida-Thouless transition line of the spin glass on a fixed connectivity random graph.
authors.affiliation: Laboratoire de Physique Théorique et Modèles Statistiques, Bâtiment 100, Université Paris-Sud, F-91405 Orsay, France.
authors.forename: A
authors.initials: A
authors.lastname: Pagnani
authors.forename: G
authors.initials: G
authors.lastname: Parisi
authors.forename: M
authors.initials: M
authors.lastname: Ratiéville