  The zero range process is of particular importance as a generic model for
domain wall dynamics of one-dimensional systems far from equilibrium. We study
this process in one dimension with rates which induce an effective attraction
between particles. We rigorously prove that for the stationary probability
measure there is a background phase at some critical density and for large
system size essentially all excess particles accumulate at a single, randomly
located site. Using random walk arguments supported by Monte Carlo simulations,
we also study the dynamics of the clustering process with particular attention
to the difference between symmetric and asymmetric jump rates. For the late
stage of the clustering we derive an effective master equation, governing the
occupation number at clustering sites.
