Comparison of the peak abundance from different cases. Upper panel: blue solid line: full N-body runs (Case 1); green circles: replacement of halos by NFW profiles (Case 2); red squares: replacement of halos by NFW profiles and randomization of halo angular positions (Case 3); cyan diamonds: fast simulations, corresponding to our model (Case 4); magenta dashed line: peaks from noise-only maps. Lower panel: we draw the upper and lower limits of error bars shifted with regard to the N-body values. This refers to the standard deviation over 4 maps (green dash-dotted line for Case 2) or 16 maps (red dashed line for Case 3, cyan solid line for Case 4). The field of view is 53.7 deg².