  The atom fluctuations statistics of an ideal, mesoscopic, Bose-Einstein
condensate is investigated from several different perspectives. By generalizing
the grand canonical analysis (applied to the canonical ensemble problem), we
obtain a self-consistent equation for the mean condensate particle number that
coincides with the microscopic result calculated from the laser master equation
approach. For the case of a harmonic trap, we obtain an analytic expression for
the condensate particle number that is very accurate at all temperatures, when
compared with numerical canonical ensemble results. Applying a similar
generalized grand canonical treatment to the variance, we obtain an accurate
result only below the critical temperature. Analytic results are found for all
higher moments of the fluctuation distribution by employing the stochastic path
integral formalism, with excellent accuracy. We further discuss a hybrid
treatment, which weds the master equation/stochastic path integral analysis
with the results obtained based on canonical ensemble quasiparticle formalism
[V. V. Kocharovsky et al., Phys. Rev. A 61, 053606 (2000)], producing
essentially perfect agreement with numerical simulation at all temperatures.
