Non-Gaussian halo abundances in the excursion set approach with
  correlated steps
  We study the effects of primordial non-Gaussianity on the large scale
structure in the excursion set approach, accounting for correlations between
steps of the random walks in the smoothed initial density field. These
correlations are induced by realistic smoothing filters (as opposed to a filter
that is sharp in k-space), but have been ignored by many analyses to date. We
present analytical arguments -- building on existing results for Gaussian
initial conditions -- which suggest that the effect of the filter at large
smoothing scales is remarkably simple, and is in fact identical to what happens
in the Gaussian case: the non-Gaussian walks behave as if they were smooth and
deterministic, or "completely correlated". As a result, the first crossing
distribution (which determines, e.g., halo abundances) follows from the
single-scale statistics of the non-Gaussian density field -- the so-called
"cloud-in-cloud" problem does not exist for completely correlated walks. Also,
the answer from single-scale statistics is simply one half that for sharp-k
walks. We explicitly test these arguments using Monte Carlo simulations of
non-Gaussian walks, showing that the resulting first crossing distributions,
and in particular the factor 1/2 argument, are remarkably insensitive to
variations in the power spectrum and the defining non-Gaussian process. We also
use our Monte Carlo walks to test some of the existing prescriptions for the
non-Gaussian first crossing distribution. Since the factor 1/2 holds for both
Gaussian and non-Gaussian initial conditions, it provides a theoretical
motivation (the first, to our knowledge) for the common practice of
analytically prescribing a ratio of non-Gaussian to Gaussian halo abundances.
