Near-optimal configurations in mean-field disordered systems

The derivation and implementation of the ε-coupling method in the framework of the cavity approach was presented. This technique allowed to explore the way the energy of a configuration varies as a function of its overlap with the ground state. The random matching problem and the mean-field diluted spin glass was studied using this technique. The de Almeida-Thouless transition line of the spin glass was calculated on a fixed connectivity random graph as a by-product of this approach.