Abstract: We consider interference experiments with two independent low dimensional bose condensates. Phase fluctuations result in shot to shot fluctuations of the interference contrast. Full distribution function of fringe visibilities is determined by higher order correlation functions within individual condensates and contains non trivial information about quantum and thermal fluctuations in the system. The problem of calculation of full distributions can be mapped to the statistics of random surfaces. We develop a general method for calculating distribution functions of the interference amplitude and apply it to one and two dimensional condensates both at zero and finite temperatures.