In the top row, we show observed projected cross-correlation measurements between the clusters and galaxies (points with error bars in red color) from left to right, for the Full, Low-z, Mid-z, and High-z cluster samples from table 3 with the fiducial absolute-magnitude cut M_z − 5log₁₀h < −18.8 for galaxy selections. Shaded colored regions show the 16th and 84th percentiles of the model predictions from the MCMC chains for each cluster sample. The dashed profile curves in the top row show contributions from off-centered clusters to projected cross-correlation measurements at the best-fitting model parameters. The second row shows constraints on the logarithmic derivative of the projected cross-correlation profiles without off-centering effects in equation (7). The third row presents constraints on the three-dimensional galaxy density profile calculated as ρ_g(r) = 〈Σ_g〉ξ_3D(r)/(2R_max) (see subsection 3.1 for more details). The last row shows the constraints on the logarithmic derivative of the three-dimensional profiles. The vertical black dashed lines denote mean values of R_200m shown in table 1 for the cluster samples. Black vertical shaded regions show model predictions from the halo–matter cross-correlation (i.e., dark matter distributions around clusters) and mass–richness relation in appendix  1 for |$R_{\rm sp}^{\rm 2D}$| in the second row and |$r_{\rm sp}^{\rm 3D}$| in the third and last rows from table 1, whereas colored vertical shaded regions show their constraints from the MCMC chains in each cluster sample. Black shaded profile regions in the second and last rows show derivative profiles from the model predictions for each cluster sample. (Color online)