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We review probabilistic approaches to the Gross-Pitaevskii theory describinginteracting dilute systems of particles. The main achievement are largedeviations principles for the mean occupation measure of a large system ofinteracting Brownian motions in a trapping potential. The corresponding ratefunctions are given as variational problems whose solution provide effectivedescriptions of the infinite system.

Interacting Brownian motions and the Gross-Pitaevskii formula