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We consider a system of $N$ bosons in the limit $N \rightarrow \infty$,interacting through singular potentials. For initial data exhibitingBose-Einstein condensation, the many-body time evolution is well approximatedthrough a quadratic fluctuation dynamics around a cubic non-linearSchr\"odinger equation of the condensate wave function. We show that thesefluctuations satisfy a (multi-variate) central limit theorem.

Central limit theorem for Bose gases interacting through singular potentials