Dark Energy Survey Year 3 results: Galaxy-halo connection from
  galaxy-galaxy lensing
  Galaxy-galaxy lensing is a powerful probe of the connection between galaxies
and their host dark matter halos, which is important both for galaxy evolution
and cosmology. We extend the measurement and modeling of the galaxy-galaxy
lensing signal in the recent Dark Energy Survey Year 3 cosmology analysis to
the highly nonlinear scales ($\sim 100$ kpc). This extension enables us to
study the galaxy-halo connection via a Halo Occupation Distribution (HOD)
framework for the two lens samples used in the cosmology analysis: a luminous
red galaxy sample (redMaGiC) and a magnitude-limited galaxy sample (MagLim). We
find that redMaGiC (MagLim) galaxies typically live in dark matter halos of
mass $\log_{10}(M_{h}/M_{\odot}) \approx 13.7$ which is roughly constant over
redshift ($13.3-13.5$ depending on redshift). We constrain these masses to
$\sim 15\%$, approximately $1.5$ times improvement over previous work. We also
constrain the linear galaxy bias more than 5 times better than what is inferred
by the cosmological scales only. We find the satellite fraction for redMaGiC
(MagLim) to be $\sim 0.1-0.2$ ($0.1-0.3$) with no clear trend in redshift. Our
constraints on these halo properties are broadly consistent with other
available estimates from previous work, large-scale constraints and
simulations. The framework built in this paper will be used for future HOD
studies with other galaxy samples and extensions for cosmological analyses.
