The clustering of peaks in a random Gaussian field

Abstract

The true peak-peak correlation function of a random Gaussian field in one and in three dimensions is examined. It is shown that the peak-peak correlation function in both one and three dimensions has zeros which do not generally coincide with the zeros of the underlying autocorrelation function. It is found that approximations to the peak-peak correlation function using the thresholded density field are generally inaccurate. The peak-peak correlation function for a linear slice through a given density field, however, is found to be an excellent approximation to the full three-dimensional result. It is concluded that correlation length of the canonical Omega = 1 cold dark matter model is too low compared to the observed cluster-cluster correlation function.