2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138231We review probabilistic approaches to the Gross-Pitaevskii theory describing interacting dilute systems of particles. The main achievement are large deviations principles for the mean occupation measure of a large system of interacting Brownian motions in a trapping potential. The corresponding rate functions are given as variational problems whose solution provide effective descriptions of the infinite system.ProbabilityMathematical Physics60F10; 60J65; 82B10; 82B26text