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tokens: 0.7 dex), which seems unlikely to be consistent with our assumed scatter of , given the small size of that sample. Figure 3. Halo-to-stellar mass ratio (the inverse of the SHMR) as a function of stellar mass. The red and blue dots denote the measurements for the low- and high-redshift samples, respectively. The red solid curve and cyan-shaded area are the best-fit SHMR relation and its 1 σ uncertainty derived by fitting our low-redshift sample combined with the results of H15. The blue solid curve is the best-fit SHMR relation of our high-redshift sample combined with H15. The red and blue dashed curves are the relations fitted by Leauthaud et al. ( 2012 ), using COSMOS measurements. We also compare our measurements with other galaxy–galaxy lensing measurements, including SDSS (Mandelbaum et al. 2006 ), CFHTLenS (H15), COSMOS X-ray clusters (Leauthaud et al. 2010 , 2012 ), and GAMA (Han et al. 2015 ). This scatter for individual systems suggests that selection effects may still be a concern, in our and other published determinations of the SHMR. For instance, Leauthaud et al. ( 2015 ) found that the CMASS sample is significantly affected by mass incompleteness, and is ∼80% complete at only in the narrow redshift range z = [0.51, 0.61]. The LOWZ sample, on the other hand, is ∼80% complete at for z = [0.15, 0.43]. If completeness is correlated with high or low stellar mass for the primary galaxy, it could mean that the true scatter is larger than what we have assumed. Follow-up studies of the individual objects in our samples, as well as data from larger forthcoming lensing surveys, will be required to determine the exact effect of these biases on the mean relation. A Chabrier ( 2003 ) IMF was assumed by the measurements of H15 , Leauthaud et al. ( 2012 ), and Han et al. ( 2015 ). Ilbert et al. ( 2010 ) investigated the possible sources of uncertainty and bias by comparing stellar mass estimates between methods. The expected difference between a Kroupa IMF and a Chabrier IMF is not significant. 5. Conclusions Combining samples of massive galaxies and clusters from the redMaPPer and LOWZ/CMASS catalogs, respectively, with the shear catalog of the CS82 survey, we have measured the projected density profiles around central galaxies at two different redshifts. We fit the lensing shear signal around these galaxies as a sum of contributions from the main DM halo, the central galaxy, centering errors and physical offsets between the galaxy and the halo, and neighboring halos. From the resulting fits, we determine the mean halo concentration as a function of mass, and also the mean relation between (central) stellar mass and halo mass (the SHMR). Our main results are as follows. 1. We find that halo concentration decreases weakly with mass, c = A ( M / M 0 ) B , with the amplitude A ∼ 5–6 and slope B ∼ −0.14. These parameter values are in good agreement with the predictions of simulations, e.g., Duffy et al. 2008 or Klypin et al. 2016 , given a