A Framework for Simultaneously Measuring Field Densities and the High-z
  Luminosity Function
  Cosmic variance from large-scale structure will be a major source of
uncertainty for galaxy surveys at z > 6, but that same structure will also
provide an opportunity to identify and study dense environments in the early
Universe. Using a robust model for galaxy clustering, we directly incorporate
large-scale densities into an inference framework that simultaneously measures
the high-z (z > 6) UV luminosity function and the average matter density of
each distinct volume in a survey. Through this framework, we forecast the
performance of several major upcoming James Webb Space Telescope (JWST) galaxy
surveys. We find that they can constrain field matter densities down to the
theoretical limit imposed by Poisson noise and unambiguously identify
over-dense (and under-dense) regions on transverse scales of tens of comoving
Mpc. We also predict JWST will measure the luminosity function with a precision
at z = 12 comparable to existing Hubble Space Telescope's constraints at z = 8
(and even better for the faint-end slope). We also find that wide-field surveys
are especially important in distinguishing luminosity function models.
