What does it take to stabilize gravitational clustering?

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.