  In the peaks approach, the formation sites of observable structures in the
Universe are identified as peaks in the matter density field. The statistical
properties of the clustering of peaks are particularly important in this
respect. In this paper, we investigate the large-separation expansion of the
correlation function of peaks in Gaussian random fields. The analytic formula
up to third order is derived, and the resultant expression can be evaluated by
a combination of one-dimensional fast Fourier transforms, which are evaluated
very fast. The analytic formula obtained perturbatively in the large-separation
limit is compared with a method of Monte-Carlo integrations, and a
complementarity between the two methods is demonstrated.
