  In this paper limiting distribution functions of field and density
fluctuations are explicitly and rigorously computed for the different phases of
the Bose gas. Several Gaussian and non-Gaussian distribution functions are
obtained and the dependence on boundary conditions is explicitly derived. The
model under consideration is the free Bose gas subjected to attractive boundary
conditions, such boundary conditions yield a gap in the spectrum. The presence
of a spectral gap and the method of the coupled thermodynamic limits are the
new aspects of this work, leading to new scaling exponents and new fluctuation
distribution functions.
