  Padmanabhan (1996) has suggested a model to relate the nonlinear two - point
correlation function to the linear two - point correlation function. In this
paper, we extend this model in two directions: (1) By averaging over the
initial Gaussian distribution of density contrasts, we estimate the spectral
dependence of the scaling between nonlinear and linear correlation functions.
(2) By using a physically motivated ansatz, we generalise the model to N-point
correlation functions and relate the nonlinear, volume averaged, N-point
correlation function $\bar\xi_N(x,a)$ with linearly extrapolated volume
averaged 2-point correlation function $\bar \xi_2(l,a)$ evaluated at a
different scale. We compare the point of transition between different regimes
obtained from our model with numerical simulations and show that the spectral
dependence of the scaling relations seen in the simulations can be easily
understood. Comparison of the calculated form of $\bar\xi_N$ with the
simulations show reasonable agreement. We discuss several implications of the
results.
