The 2D density distribution as a function of radial offset r and flux difference S_in − S_out in the simulated unclustered COSMOS field at 250 μm (SXT: top panels; SF: bottom panels). The left-hand panels show the density distribution of all matches between the input and output catalogue. The middle panels show the density distribution of all matches between the input and the randomized output catalogue. The right-hand panels show the difference between the left and middle panels (note the changing colour scale) which can be approximated as the 2D density distribution of the real input–output matches.