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Using an Eulerian perturbative calculation, we show that the distribution ofrelative pairwise velocities which arises from gravitational instability ofGaussian density fluctuations has asymmetric (skewed) exponential tails. Thenegative skewness is induced by the negative mean streaming velocity of pairs(the infall prevails over expansion), while the exponential tails arise becausethe relative pairwise velocity is a number, not volume weighted statistic. Thederived probability distribution is compared with N-body simulations and shownto provide a reasonable fit.Comment: 14 pages, 1 figure, accepted for publication in ApJ letter

Skewed Exponential Pairwise Velocities from Gaussian Initial Conditions