Left: cumulative histogram of the overdensity contrast δ₃₅₀ (blue) of each Planck field (based on 350μm SPIRE sources). Overdensities are fairly large, with 59 fields having δ₃₅₀> 3. Right: Cumulative (normalized) statistical significance in σ derived from the density maps. Blue represents all our SPIRE sources, red represents only redder SPIRE sources, defined by S₃₅₀/S₂₅₀> 0.7 and S₅₀₀/S₃₅₀> 0.6, and orange 500 random fields in Lockman. Most of our fields have a significance greater than 4σ, and the significance is higher still for the redder sources. See Sect. 4.2 for details.