  These lecture notes discuss two effects which contribute to the reduction of
the interference fringe contrast in matter interferometers. The first effect is
the shot noise arising from a finite number of atoms used in experiments.
Focusing on a single shot measurement we provide explicit calculations of the
full distribution functions of the fringe contrast for the interference of
either the coherent or the number states of atoms. Another mechanism of the
suppression of the amplitude of interference fringes discussed in these lecture
notes is the quantum and thermal fluctuations of the order parameter in low
dimensional condensates. We summarize recent theoretical and experimental
studies demonstrating that suppression of the interference fringe contrast and
its shot to shot variations can be used to study correlation functions within
individual condensates. We also discuss full distribution functions of the
fringe amplitudes for one and two dimensional condensates and review their
connection to high order correlation functions. We point out intriguing
mathematical connections between the distribution functions of interference
fringe amplitudes and several other problems in field theory, systems of
correlated electrons, and statistical physics.
