  We examine the peculiar velocity distribution function of galaxies in
cosmological many-body gravitational clustering. Our statistical mechanical
approach derives a previous basic assumption and generalizes earlier results to
galaxies with haloes. Comparison with the observed peculiar velocity
distributions indicates that individual massive galaxies are usually surrounded
by their own haloes, rather than being embedded in common haloes. We then
derive the density of energy states, giving the probability that a randomly
chosen configuration of N galaxies in space is bound and virialized.
Gravitational clustering is very efficient. The results agree well with the
observed probabilities for finding nearby groups containing N galaxies. A
consequence is that our local relatively low mass group is quite typical, and
the observed small departures from the local Hubble flow beyond our group are
highly probable.
