A theoretical framework for combining techniques that probe the link
  between galaxies and dark matter
  We develop a theoretical framework that combines measurements of
galaxy-galaxy lensing, galaxy clustering, and the galaxy stellar mass function
in a self-consistent manner. While considerable effort has been invested in
exploring each of these probes individually, attempts to combine them are still
in their infancy despite the potential of such combinations to elucidate the
galaxy-dark matter connection, to constrain cosmological parameters, and to
test the nature of gravity. In this paper, we focus on a theoretical model that
describes the galaxy-dark matter connection based on standard halo occupation
distribution techniques. Several key modifications enable us to extract
additional parameters that determine the stellar-to-halo mass relation and to
simultaneously fit data from multiple probes while allowing for independent
binning schemes for each probe. In a companion paper, we demonstrate that the
model presented here provides an excellent fit to galaxy-galaxy lensing, galaxy
clustering, and stellar mass functions measured in the COSMOS survey from z=0.2
to z=1.0. We construct mock catalogs from numerical simulations to investigate
the effects of sample variance and covariance on each of the three probes.
Finally, we analyze and discuss how trends in each of the three observables
impact the derived parameters of the model. In particular, we investigate the
various features of the observed galaxy stellar mass function (low-mass slope,
plateau, knee, and high-mass cut-off) and show how each feature is related to
the underlying relationship between stellar and halo mass. We demonstrate that
the observed plateau feature in the stellar mass function at Mstellar~2x10^10
Msun is due to the transition that occurs in the stellar-to-halo mass relation
at Mhalo ~ 10^12 Msun from a low-mass power-law regime to a sub-exponential
function at higher stellar mass.
