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Satellite galaxies in rich clusters are subject to numerous physicalprocesses that can significantly influence their evolution. However, thetypical L* satellite galaxy resides in much lower mass galaxy groups, where theprocesses capable of altering their evolution are generally weaker and have hadless time to operate. To investigate the extent to which satellite and centralgalaxy evolution differs, we separately model the stellar mass - halo mass (M*-Mh) relation for these two populations over the redshift interval 0 < z < 1.This relation for central galaxies is constrained by the galaxy stellar massfunction while the relation for satellite galaxies is constrained againstrecent measurements of the galaxy two-point correlation function (2PCF). At z ~0 the satellites, on average, have ~10% larger stellar masses at fixed peaksubhalo mass compared to central galaxies of the same halo mass. This isrequired in order to reproduce the observed stellar mass-dependent 2PCF andsatellite fractions. At low masses our model slightly under-predicts thecorrelation function at ~1 Mpc scales. At z ~ 1 the satellite and centralgalaxy M*-Mh relations are consistent within the errors, and the model providesan excellent fit to the clustering data. At present, the errors on theclustering data at z ~ 2 are too large to constrain the satellite model. Asimple model in which satellite and central galaxies share the same M*-Mhrelation is able to reproduce the extant z ~ 2 clustering data. We speculatethat the striking similarity between the satellite and central galaxy M*-Mhrelations since z ~ 2 arises because the central galaxy relation evolves veryweakly with time and because the stellar mass of the typical satellite galaxyhas not changed significantly since it was accreted. [Abridged]

The Strikingly Similar Relation between Satellite and Central Galaxies and Their Dark Matter Halos Since z=2