The Local Bias Model in the Large Scale Halo Distribution
  We explore the biasing in the clustering statistics of halos as compared to
dark matter (DM) in simulations. We look at the second and third order
statistics at large scales of the (intermediate) MICEL1536 simulation and also
measure directly the local bias relation h = f({\delta}) between DM
fluctuations, {\delta}, smoothed over a top-hat radius Rs at a point in the
simulation and its corresponding tracer h (i.e. halos) at the same point. This
local relation can be Taylor expanded to define a linear (b1) and non-linear
(b2) bias parameters. The values of b1 and b2 in the simulation vary with Rs
approaching a constant value around Rs > 30 - 60 Mpc/h. We use the local
relation to predict the clustering of the tracer in terms of the one of DM.
This prediction works very well (about percent level) for the halo 2-point
correlation {\xi}(r_12) for r_12 > 15 Mpc/h, but only when we use the biasing
values that we found at very large smoothing radius Rs > 30 - 60 Mpc/h. We find
no effect from stochastic or next to leading order terms in the f({\delta})
expansion. But we do find some discrepancies in the 3-point function that needs
further understanding. We also look at the clustering of the smoothed moments,
the variance and skewness which are volume average correlations and therefore
include clustering from smaller scales. In this case, we find that both next to
leading order and discreetness corrections (to the local model) are needed at
the 10 - 20% level. Shot-noise can be corrected with a term {\sigma}e^2/n where
{\sigma}e^2 < 1, i.e., always smaller than the Poisson correction. We also
compare these results with the peak-background split predictions from the
measured halo mass function. We find 5-10% systematic (and similar statistical)
errors in the mass estimation when we use the halo model biasing predictions to
calibrate the mass.
