Scaling Relations for Gravitational Collapse in Two Dimensions

It is known that radial collapse around density peaks can explain the key features of evolution of correlation function in gravitational clustering in three dimensions. The same model also makes specific predictions for two dimensions. In this paper we test these predictions in two dimensions with the help of N-Body simulations. We find that there is no stable clustering in the extremely non-linear regime, but a nonlinear scaling relation does exist and can be used to relate the linear and the non-linear correlation function. In the intermediate regime, the simulations agree with the model.