MEDDLING THE EVOLUTION OF CORRELATION-FUNCTIONS IN GRAVITATIONAL CLUSTERING

Padmanabhan has suggested a model to relate the non-linear two-point c orrelation function to the linear two-point correlation function. fn t his paper, we extend this model in two directions: (1) by averaging ov er the initial Gaussian distribution of density contrasts, we estimate the spectral dependence of the scaling between nonlinear and linear c orrelation functions; (2) by using a physically motivated Ansatz, we g eneralize the model to N-point correlation functions and relate the no n-linear, volume averaged N-point correlation function <(xi)over bar>( N)(x, a) with the linearly extrapolated volume averaged two-point corr elation function <(xi)over bar>(2)(l, a) evaluated at a different scal e. We compare the point of transition between the different regimes ob tained from our model with that from numerical simulations, and show t hat the spectral dependence of the scaling relations seen in the simul ations can be easily understood. A comparison of the calculated form o f <(xi)over bar>(N) with the simulations shows reasonable agreement. W e discuss several implications of the results.