Statistics of wave dynamics in random media

We measure the joint distribution of the energy transmission coefficient epsilon(ab) and the single channel delay time tau(ab) for microwave radiation propagating through a random medium in the limit of zero pulse bandwidth. For fixed epsilon(ab) the distribution of tau(ab) is Gaussian with variance inversely proportional to epsilon(ab) In contradistinction to tau(ab), the dynamic matrix element epsilon(ab) tau(ab) has substantial long-range correlation with frequency shift. We present a new dynamic theory for a Gaussian process, which is in excellent agreement with experiment.