Each row corresponds to one SMG. Left panel: δ_g versus radius, centred at the target SMG (see Sect. 3.1.1). The errors shown are Poisson errors. The number of sources found in a circular area (N_r), and the δ_g = 0 line are indicated. Also indicated are the points with Poisson probability p ≤ 0.05, as listed in the legend (see Sect. 3.1.1 for details). Middle panel: Voronoi tessellation analysis (VTA; blue lines) shown around each target SMG indicated by the thick red circle. Overdense VTA cells are coloured yellow. The area and density of the cells depend on the number of galaxies in the given redshift range (Δz_phot), indicated above the panel. The overdensity centre is shown by the red cross, and the radius within which it was computed is indicated by the black circle (see Sect. 3.1.2 for details). Regions outlined by grey lines and curves indicate the masked areas in the COSMOS photometric catalogue. Right panel: the top panel shows δ_g versus radius, centred at the overdensity (indicated by the red cross in the middle panel). The SMG’s projected distance from the centre is indicated by the red downwards pointing arrow. The horizontal line indicates the value δ_g = 0. The meaning of various symbols and linestyles is listed in the legend. The bottom panel shows the significance of the overdensity (δ_g/σ_{δg = 0}) as a function of radius. The dashed horizontal line designates the threshold beyond which the false detection probability is ≤20% (see Sect. 3.1.3 for details).