# The self similarity of weak lensing peaks

## TL;DR

This paper investigates the statistics of weak lensing convergence peaks, revealing their self-similar clustering behavior and how their abundance and clustering can jointly constrain cosmological parameters like _m and _8.

## Contribution

It introduces accurate models for peak abundance and clustering, demonstrating their potential to break cosmological parameter degeneracies.

## Key findings

- Peak abundance depends on cosmology within 3% accuracy.
- Peak 2PCFs exhibit self-similar behavior after rescaling.
- Combined peak statistics can break _m-_8 degeneracy.

## Abstract

We study the statistics of weak lensing convergence peaks, such as their abundance and two-point correlation function (2PCF), for a wide range of cosmological parameters $\Omega_m$ and $\sigma_8$ within the standard $\Lambda$CDM paradigm, focusing on intermediate-height peaks with signal-to-noise ratio (SNR) of $1.5$ to $3.5$. We find that the cosmology dependence of the peak abundance can be described by a one-parameter fitting formula that is accurate to within $\sim3\%$. The peak 2PCFs are shown to feature a self-similar behaviour: if the peak separation is rescaled by the mean inter-peak distance, catalogues with different minimum peak SNR values have identical clustering, which suggests that the peak abundance and clustering are closely interconnected. A simple fitting model for the rescaled 2PCF is given, which together with the peak abundance model above can predict peak 2PCFs with an accuracy better than $\sim5\%$. The abundance and 2PCFs for intermediate peaks have very different dependencies on $\Omega_m$ and $\sigma_8$, implying that their combination can be used to break the degeneracy between these two parameters.