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
(zs ¼ 1.0–2.0) we also provide results for maps inferred from lensing of the cosmic microwave background
(CMB), i.e., zs ¼ 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 fsky ¼ 0.35, can range between 6–12 depending on the value of the intrinsic
ellipticity distribution parameter σϵ ¼ 0.3–1.0. For reconstructed κ maps using an ideal CMB survey the
S=N ≈ 1.8. We also found that a 10% deviation in σ8 can be detected using IB for the optimistic case of
σϵ ¼ 0.3 with a S=N ≈ 5. The S/N for such detection in case of ΩM is lower.