  We consider a problem of interference between two independent condensates,
which lack true long range order. We show that their interference pattern
contains information about correlation functions within each condensate. As an
example we analyze the interference between a pair of one dimensional
interacting Bose liquids. We find universal scaling of the average fringe
contrast with system size and temperature that depends only on the Luttinger
parameter. Moreover the full distribution of the fringe contrast, which is also
equivalent to the full counting statistics of the interfering atoms, changes
with interaction strength and lends information on high order correlation
functions. We also demonstrate that the interference between two-dimensional
condensates at finite temperature can be used as a direct probe of the
Kosterlitz-Thouless transition. Finally, we discuss generalization of our
results to describe the intereference of a periodic array of independent
fluctuating condensates.
