Here we present a novel N-body simulation technique that allows us to compute ensemble statistics on a local basis , directly relating halo properties to their environment .
This is achieved by the use of an ensemble simulation in which the otherwise independent realizations share the same fluctuations above a given cut-off scale .
This produces a constrained ensemble where the LSS is common to all realizations while having an independent halo population .
By generating a large number of semi-independent realizations we can effectively increase the local halo density by an arbitrary factor thus breaking the fundamental limit of the finite halo density ( for a given halo mass range ) determined by the halo mass function .

This technique allows us to compute local ensemble statistics of the matter/halo distribution at a particular position in space , removing the intrinsic stochasticity in the halo formation process and directly relating halo properties to their environment .
This is a major improvement over global descriptors of the matter/halo distribution which can not resolve local variations .

We introduce the Multum In Parvo ( MIP ) constrained ensemble simulation consisting of 220 realizations of 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 MIP simulation stands apart from all previous N-body simulations in its unprecedented high equivalent particle density and local halo density .

We illustrate the potential of the technique presented here by computing the local mass function at several characteristic environments and along a path from the center of a void to its border .
We can study for the first time the effect of local environment in the height , shape and characteristic mass of the halo mass function .

Future observations will provide detailed models of the galaxy density distribution allowing the use of constrained realizations in combination with ensemble simulations to derive accurate “ mean ensemble ” properties of the local Universe .