  We develop a generic phenomenological model to describe the fluctuations on
top of a non-equilibrium Bose-Einstein condensate. Analytic expressions are
obtained for the momentum distribution of the non-condensed cloud and for the
long-distance behavior of the spatial coherence in the different
dimensionalities. Comparison of our predictions with available experimental
data on condensates of exciton-polaritons and on surface-emitting planar laser
devices is finally made.
