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 e ects of a realistic ltering of the density eld, a mass-dependent threshold for collapse, and the prescription from peak theory that halos tend to form around density maxima. We nd that our approximations work excellently for diverse power spectra, collapse thresholds and density lters. Moreover, when adopting a cold dark matter power spectra, a tophat ltering 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.