Distribution of the centroid offset between mass and light and the local galaxy density, Σ. Left: Distributions for variants of Σ₁₀ based on the number of galaxies chosen and applying a flux selection. Right: Distributions for various weighting schemes in the Σ definition (i.e., definitions B, C, and D). The very weak to weak correlations for all the definitions of Σ robustly indicate that the local galaxy density has no impact on the centroid offset between mass and light.