One simulation to have them all: performance of the Bias Assignment
  Method against N-body simulations
  In this paper we demonstrate that the information encoded in \emph{one}
single (sufficiently large) $N$-body simulation can be used to reproduce
arbitrary numbers of halo catalogues, using approximated realisations of dark
matter density fields with different initial conditions. To this end we use as
a reference one realisation (from an ensemble of $300$) of the Minerva $N$-body
simulations and the recently published Bias Assignment Method to extract the
local and non-local bias linking the halo to the dark matter distribution. We
use an approximate (and fast) gravity solver to generate $300$ dark matter
density fields from the down-sampled initial conditions of the reference
simulation and sample each of these fields using the halo-bias and a kernel,
both calibrated from the arbitrarily chosen realisation of the reference
simulation. We show that the power spectrum, its variance and the three-point
statistics are reproduced within $\sim 2\%$ (up to $k\sim1.0\,h\,{\rm
Mpc}^{-1}$), $\sim 5-10\%$ and $\sim 10\%$, respectively. Using a model for the
real space power spectrum (with three free bias parameters), we show that the
covariance matrices obtained from our procedure lead to parameter uncertainties
that are compatible within $\sim 10\%$ with respect to those derived from the
reference covariance matrix, and motivate approaches that can help to reduce
these differences to $\sim 1\%$. Our method has the potential to learn from one
simulation with moderate volumes and high-mass resolution and extrapolate the
information of the bias and the kernel to larger volumes, making it ideal for
the construction of mock catalogues for present and forthcoming observational
campaigns such as Euclid or DESI.
