Galaxy Correlation Function and Local Density from Photometric Redshifts
  Using the Stochastic Order Redshift Technique (SORT)
  The stochastic order redshift technique (SORT) is a simple, efficient, and
robust method to improve cosmological redshift measurements. The method relies
upon having a small ($\sim$10 per cent) reference sample of high-quality
redshifts. Within pencil-beam-like sub-volumes surrounding each galaxy, we use
the precise dN/d$z$ distribution of the reference sample to recover new
redshifts and assign them one-to-one to galaxies such that the original rank
order of redshifts is preserved. Preserving the rank order is motivated by the
fact that random variables drawn from Gaussian probability density functions
with different means but equal standard deviations satisfy stochastic ordering.
The process is repeated for sub-volumes surrounding each galaxy in the survey.
This results in every galaxy with an uncertain redshift being assigned multiple
"recovered" redshifts from which a new redshift estimate can be determined. An
earlier paper applied SORT to a mock Sloan Digital Sky Survey at $z \lesssim$
0.2 and accurately recovered the two-point correlation function on scales
$\gtrsim$4 $h^{-1}$Mpc. In this paper, we test the performance of SORT in
surveys spanning the redshift range 0.75$<z<$2.25. We used two mock surveys
extracted from the Small MultiDark-Planck and Bolshoi-Planck N-body simulations
with dark matter haloes that were populated by the Santa Cruz semi-analytic
model. We find that SORT is able to improve redshift estimates and recover
distinctive large-scale features of the cosmic web. Further, it provides
unbiased estimates of the redshift-space two-point correlation function
$\xi(s)$ on scales $\gtrsim$2.5 $h^{-1}$Mpc, as well as local densities in
regions of average or higher density. This may allow improved understanding of
how galaxy properties relate to their local environments.
