Statistics of Dark Matter Halos in the Excursion Set Peak Framework
  We derive approximated, yet very accurate analytical expressions for the
abundance and clustering properties of dark matter halos in the excursion set
peak framework; the latter relies on the standard excursion set approach, but
also includes the effects of a realistic filtering of the density field, a
mass-dependent threshold for collapse, and the prescription from peak theory
that halos tend to form around density maxima. We find that our approximations
work excellently for diverse power spectra, collapse thresholds and density
filters. Moreover, when adopting a cold dark matter power spectra, a tophat
filtering and a mass-dependent collapse threshold (supplemented with
conceivable scatter), our approximated halo mass function and halo bias
represent very well the outcomes of cosmological $N-$body simulations.
