The MIP Ensemble Simulation: Local Ensemble Statistics in the Cosmic Web
  We present a new technique that allows us to compute ensemble statistics on a
local basis, directly relating halo properties to their local environment. This
is achieved by the use of a correlated ensemble in which the Large Scale
Structure is common to all realizations while having each an independent halo
population. The correlated ensemble can be stacked, effectively increasing the
halo number density by an arbitrary factor, thus breaking the fundamental limit
in the halo number density given by the haloe mass function. This technique
allows us to compute \textit{local ensemble statistics} of the matter/haloe
distribution at any position in the simulation box, while removing the
intrinsic stochasticity in the halo formation process and directly relating
halo properties to their environment.
  We introduce the \textit{Multum In Parvo} (MIP) correlated ensemble
simulation consisting of 220 realizations on a 32 h$^{-1}$ Mpc box with $256^3$
particles each. This is equivalent in terms of effective volume and number of
particles to a box of $\sim 193$ h$^{-1}$ Mpc of side with $\sim 1540^3$
particles containing $\sim 5\times 10^6$ haloes with a minimum mass of $3.25
\times 10^9$ h$^{-1}$ M$_{\odot}$.
  The potential of the technique presented here is illustrated by computing the
local ensemble statistics of the halo ellipticity and halo shape-LSS alignment.
We show that, while there are general trends in the ellipticity and alignment
of haloes with their LSS, there are also significant spatial variations which
has important implications for observational studies of galaxy shape and
alignment.
