We provide a systematic study of the position-dependent correlation function in weak-lensing convergence maps and its relation to the squeezed limit of the three-point correlation function (3PCF) using state-of-the-art numerical simulations. We relate the position-dependent correlation function to its harmonic counterpart, i.e., the position-dependent power spectrum or equivalently the integrated bispectrum (IB). We use a recently proposed improved fitting function, BiHalofit, for the bispectrum to compute the theoretical predictions as a function of source redshifts. In addition to low redshift results ($z_s=1.0–2.0$) we also provide results for maps inferred from lensing of the cosmic microwave background (CMB), i.e., $z_s=1100$. We include a Euclid-type realistic survey mask and noise. In agreement with the recent studies on the position-dependent power spectrum, we find that the results from simulations are consistent with the theoretical expectations when appropriate corrections are included. Performing a rough estimate, we find that the signal-to-noise (S/N) for the detection of position-dependent correlation function from Euclid-type mask with $f_{\mathrm{sky}}=0.35$, can range between 6–12 depending on the value of the intrinsic ellipticity distribution parameter ${\sigma }_{\epsilon }=0.3–1.0$. For reconstructed $\kappa$ maps using an ideal CMB survey the $\mathrm{S}/\mathrm{N}\approx 1.8$. We also found that a 10% deviation in ${\sigma }_8$ can be detected using IB for the optimistic case of ${\sigma }_{\epsilon }=0.3$ with a $\mathrm{S}/\mathrm{N}\approx 5$. The S/N for such detection in case of ${\mathrm{\Omega }}_M$ is lower.

• Received 14 April 2021
• Accepted 19 December 2022

DOI:https://doi.org/10.1103/PhysRevD.107.043516