ELUCID - Exploring the Local Universe with reConstructed Initial Density
  field III: Constrained Simulation in the SDSS Volume
  A method we developed recently for the reconstruction of the initial density
field in the nearby Universe is applied to the Sloan Digital Sky Survey Data
Release 7. A high-resolution N-body constrained simulation (CS) of the
reconstructed initial condition, with $3072^3$ particles evolved in a 500 Mpc/h
box, is carried out and analyzed in terms of the statistical properties of the
final density field and its relation with the distribution of SDSS galaxies. We
find that the statistical properties of the cosmic web and the halo populations
are accurately reproduced in the CS. The galaxy density field is strongly
correlated with the CS density field, with a bias that depend on both galaxy
luminosity and color. Our further investigations show that the CS provides
robust quantities describing the environments within which the observed
galaxies and galaxy systems reside. Cosmic variance is greatly reduced in the
CS so that the statistical uncertainties can be controlled effectively even for
samples of small volumes.
