  An analytical understanding of the strongly nonlinear regime of gravitational
collapse has been difficult to achieve. The only insight has been the stable
clustering hypothesis, which assumes that the number of neighbors for objects
averaged over small length scales is constant in time. Our recently proposed
analytic halo model for N-point correlation functions now provides a tool for
calculating gravitational clustering properties in the strongly nonlinear
regime. This model also provides a new physical framework for an independent
evaluation of the validity of the stable clustering hypothesis. We derive the
asymptotic nonlinear behavior of the N-point correlation functions and pairwise
peculiar velocities in terms of dark matter halo properties. We show that these
statistics exhibit stable clustering only when the halo mass function and halo
density profile obey specific relations. The long-cherished stable clustering
hypothesis therefore is not necessarily realized in practice.
