It takes two to know one: computing accurate one-point PDF covariances from effective two-point PDF models

One-point probability distribution functions (PDFs) of the cosmic matter density are powerful cosmological probes that extract non-Gaussian properties and complement two-point statistics. Computing covariance one-point PDFs is key for building a robust galaxy survey analysis upcoming surveys like Euclid Rubin Observatory LSST requires good models characterising spatial correlations. In this work, we obtain accurate PDF covariances using effective shifted lognormal mildly weak lensing convergence validate our predictions against large sets Gaussian maps. We show how dominant effects in matrix capturing super-sample arise from large-separation expansion discuss differences between obtained small patches full sky Finally, describe formalism can be extended to characterise 3D-dimensional spectroscopic fields 3D as an example. simulated boxes with fixed overall supplemented missing effect by relying on theoretical validated separate-universe style simulations.