Halo bias in the excursion set approach with correlated steps
  In the Excursion Set approach, halo abundances and clustering are closely
related. This relation is exploited in many modern methods which seek to
constrain cosmological parameters on the basis of the observed spatial
distribution of clusters. However, to obtain analytic expressions for these
quantities, most Excursion Set based predictions ignore the fact that, although
different k-modes in the initial Gaussian field are uncorrelated, this is not
true in real space: the values of the density field at a given spatial
position, when smoothed on different real-space scales, are correlated in a
nontrivial way. We show that when the excursion set approach is extended to
include such correlations, then one must be careful to account for the fact
that the associated prediction for halo bias is explicitly a real-space
quantity. Therefore, care must be taken when comparing the predictions of this
approach with measurements in simulations, which are typically made in
Fourier-space. We show how to correct for this effect, and demonstrate that
ignorance of this effect in recent analyses of halo bias has led to incorrect
conclusions and biased constraints.
