  In the gravitational evolution of a cold infinite particle distribution,
two-body interactions can be predominant at early times: we show that, by
treating the simple case of a Poisson particle distribution in a static
universe as an ensemble of isolated two-body systems, one may capture the
origin of the first non-linear correlated structures. The developed power-law
like behavior of the two-point correlation function is then simply related to
the functional form of the time evolved nearest-neighbor probability
distribution, whose time dependence can be computed by using Liouville theorem
for the gravitational two-body problem. We then show that a similar dynamical
evolution is also found in a large-scale ordered distribution, which has
striking similarities to the case of a cosmological CDM simulation which we
also consider.
