The large-separation expansion of peak clustering in Gaussian random fields

TL;DR

This paper derives an analytic third-order formula for the large-separation correlation function of peaks in Gaussian random fields, enabling fast evaluation and comparison with Monte-Carlo methods, advancing understanding of cosmic structure formation.

Contribution

It provides the first third-order analytic expansion for peak clustering in Gaussian fields, combining perturbative and numerical methods for improved accuracy.

Findings

Analytic formula evaluated efficiently using FFTs.

Good agreement between perturbative and Monte-Carlo methods.

Enhanced understanding of peak clustering at large separations.

Abstract

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.