Statistical characteristics of the dispersive, long-wavelength, and difference marginal velocity distributions.

Statistics are shown for the following marginal velocity distributions: dispersive Eq. (32), long-wavelength Eq. (36), and difference Eq. (51). The characteristic velocities for these three distributions are , , and , respectively. , , and are the mean, standard deviation, and skewness in , respectively. In order to achieve a compact notation, we have defined , where for . Further, we use with and , , and . For one finds , as the difference propagator turns into the dispersive one. We have not found a closed analytic form for the mode and median of the difference distribution, but they can be computed numerically. Further definitions needed for the evaluation of the difference distribution statistics are collected in Eqns. (43) and (52).