Results of the analytic shot-noise correction applied to the toy model for which only one point in a pair is weighted by the density contrast δ_Rf. The upper panel shows the full weighted correlation function 1 + W_f as a mean over the five Covmos realisations, where different colours denote different levels of depletion. Errorbars are computed by taking the mean standard deviation over five realisations. To obtain the depleted catalogues we took the mean over 100 depletions. The lower panel shows the relative difference of the analytically corrected result to the undepleted case as a red dashed line. The solid black line refers to the relative difference of the depletion level 1.7% to the undepleted case, which illustrates the effect of no correction. Horizontal dashed lines in black indicate levels of relative differences of ±1% and the vertical dashed line in grey refers to side length of one grid cell. We used 64 grid cells per dimension and a PCS MAS to obtain the density field on the grid.