The Cosmic Web Around The Brightest Galaxies During The Epoch Of
  Reionization
  The most luminous galaxies at high-redshift are generally considered to be
hosted in massive dark-matter halos of comparable number density, hence
residing at the center of overdensities/protoclusters. We assess the validity
of this assumption by investigating the clustering around the brightest
galaxies populating the cosmic web at redshift $z\sim8-9$ through a combination
of semi-analytic modeling and Monte Carlo simulations of mock Hubble Space
Telescope WFC3 observations. The innovative aspect of our approach is the
inclusion of a log-normal scatter parameter $\Sigma$ in the galaxy luminosity
versus halo mass relation, extending to high-$z$ the conditional luminosity
function framework extensively used at low redshift. Our analysis shows that
the larger the value of $\Sigma$, the less likely that the brightest source in
a given volume is hosted in the most massive halo, and hence the weaker the
overdensity of neighbors. We derive a minimum value of $\Sigma$ as a function
of redshift by considering stochasticity in the halo assembly times, which
affects galaxy ages and star formation rates in our modeling. We show that
$\Sigma_{min}(z)\sim0.15-0.3$, with $\Sigma_{min}$ increasing with redshift as
a consequence of shorter halo assembly periods at higher redshifts. Current
observations ($m_{AB}\sim27$) of the environment of spectroscopically confirmed
bright sources at $z>7.5$ do not show strong evidence of clustering and are
consistent with our modeling predictions for $\Sigma\geq\Sigma_{min}$. Deeper
future observations reaching $m_{AB}\sim28.2-29$ would have the opportunity to
clearly quantify the clustering strength, and hence to constrain $\Sigma$,
investigating the physical processes that drive star formation in the early
Universe.
