Three-point correlations of peaks in cosmological density fields

Abstract

We extend previous work on the clustering properties of Gaussian random noise, and apply the results to cosmological density fields. We compute the three-point correlation function of regions where a Gaussian random process exceeds some threshold level. In the case where the threshold is sharp we find that the results are not well described by Kirkwood scaling; this contrasts with previously published work. As an alternative to the high-region prescription, we explore the clustering of local maxima of the density field. (Technical complexities involved with the treatment of local maxima restrict us to the simplified case of noise defined on a one-dimensional domain.) In this case, we find that the three-point correlation function follows a roughly hierarchical relationship with the two-point function in interesting scales