EVOLUTION OF THE PAIRWISE PECULIAR VELOCITY DISTRIBUTION FUNCTION IN LAGRANGIAN PERTURBATION-THEORY

The statistical distribution of the radial pairwise peculiar velocity of galaxies is known to have an exponential form as implied by observa tions and explicitly shown in N-body simulations. Here we calculate it s statistical distribution function using a Lagrangian perturbation th eory assuming that the primordial density fluctuations are Gaussian di stributed. We show that the exponential distribution is realized as a transient phenomenon on megaparsec scales in the standard cold-dark-ma tter model.