Condensate statistics in interacting and ideal dilute Bose gases

We obtain analytical formulas for the statistics, in particular, for the ch aracteristic function and all cumulants, of the Bose-Einstein condensate in dilute weakly interacting and ideal equilibrium gases in the canonical ens emble via the particle-number-conserving operator formalism of Girardeau an d Arnowitt. We prove that the ground-state occupation statistics is not Gau ssian even in the thermodynamic limit. We calculate the effect of Bogoliubo v coupling on suppression of ground-state occupation fluctuations and show that they are governed by a pair-correlation, squeezing mechanism.