Statistical Physics of Bose-Einstein Condensation

We review a progress in understanding of statistical properties of a quantum degenerate Bose gas. We show how the Maxwell demon ensemble helps to compute fluctuations of the Bose-Einstein condensate of an ideal Bose gas according to the microcanonical ensemble. Then, we review a method of measuring these fluctuations. Using a soluble model of interacting Bose gas we also stress the importance of higher-order correlation functions. Finally, we review our novel computational method of studying an interacting Bose gas near its critical temperature