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Skewed Exponential Pairwise Velocities from Gaussian Initial Conditions

Using an Eulerian perturbative calculation, we show that the distribution of relative pairwise velocities that arises from the gravitational instability of Gaussian density fluctuations has asymmetric (skewed) exponential tails. The negative skewness is induced by the negative mean streaming velocity of pairs (the infall prevails over expansion), while the exponential tails arise because the relative pairwise velocity is a number-weighted, not a volume-weighted, statistic. The derived probability distribution is compared with N-body simulations and is shown to provide a reasonable fit.