Scale dependent halo bias in the excursion set approach
  If one accounts for correlations between scales, then nonlocal, k-dependent
halo bias is part and parcel of the excursion set approach, and hence of halo
model predictions for galaxy bias. We present an analysis that distinguishes
between a number of different effects, each one of which contributes to
scale-dependent bias in real space. We show how to isolate these effects and
remove the scale dependence, order by order, by cross-correlating the halo
field with suitably transformed versions of the mass field. These
transformations may be thought of as simple one-point, two-scale measurements
that allow one to estimate quantities which are usually constrained using
n-point statistics. As part of our analysis, we present a simple analytic
approximation for the first crossing distribution of walks with correlated
steps which are constrained to pass through a specified point, and demonstrate
its accuracy. Although we concentrate on nonlinear, nonlocal bias with respect
to a Gaussian random field, we show how to generalize our analysis to more
general fields.
